How to Calibrate Liquidity Buffers Under Normal and Stressed Conditions

Liquidity risk: how to calibrate liquidity buffers under normal and stressed conditions

Walter Mathian

1. DEFINING, MEASURING AND MANAGING LIQUIDITY RISK ...... 5

1.1. HOW TO DEFINE LIQUIDITY RISK? ...... 5 1.2. LIQUIDITY RISK FOR INSURANCE COMPANIES ...... 6 1.3. HOW TO MANAGE LIQUIDITY RISK? ...... 7 1.3.1. Standards for managing liquidity risk ...... 7 1.3.2. Different strategies to reduce structural liquidity sources and contingent liquidity risk ...... 9 1.3.3. The crucial role played by the counterbalancing capacity (CBC) and liquid buffers ...... 10 1.3.3.1. The counterbalancing capacity: from the short term horizon to the long term horizon ...... 10 1.3.3.2. The liquid buffer ...... 10 1.3.4. Contingency planning ...... 14 1.4. HOW TO MEASURE LIQUIDITY RISK UNDER NORMAL CONDITIONS? ...... 14 2. A CONCEPTUAL FRAMEWORK TO ANALYSE THE MATURITY MISMATCH ...... 19

2.1. THE APPROACH DEFINED BY ROBERT FIEDLER ...... 19 2.1.1. Description of the conceptual framework ...... 19 2.1.1.1. Introduction of a few basic concepts...... 19 2.1.1.2. Characterisation of cash flows based on their uncertainty ...... 21 2.1.1.3. Defining the forward looking exposure ...... 22 2.1.1.4. The main aim of liquidity management: ensure a possible excess of liquidity at any time ...... 23 2.1.1.5. Defining scenarios and strategies to compute the FLE ...... 25 2.1.2. Main liquidity drivers to be taken into consideration when modelling future cash flows ...... 25 2.2. BEHAVIOURAL MODELS AND SPECIFIC EXAMPLES ON SOME LIQUIDITY DRIVERS ...... 26 2.2.1. General introduction to behavioural models ...... 26 2.2.2. The specific issue of assets and liabilities without a maturity, NoMALs, and some examples of approaches used to model their maturity...... 28 2.2.2.1. Replicating portfolio models (e. g. Bardenhewer)...... 28 2.2.2.2. The option adjusted spread (e.g. Jarrow‐van Deventer) ...... 29 2.2.2.3. Using a parametric survival model (Musakwa) ...... 30 2.2.3. Some more specific examples of NoMALs ...... 31 2.2.3.1. Sight deposits ...... 31 2.2.3.2. Assets with prepayment option ...... 33 2.2.3.3. New production modelling ...... 34 3. THE SUPERVISORY APPROACH OF LIQUIDITY AND ITS LATEST UPDATE, BASEL III ...... 34

3.1. A HISTORY OF THE SUPERVISORY APPROACH REGARDS LIQUIDITY ...... 34 3.2. NEW RATIOS: LCR AND NSFR ...... 35 3.2.1. Description of both metrics ...... 35 3.2.1.1. LCR ...... 35 3.2.1.2. NSFR ...... 36 3.2.2. Some thoughts around LCR and NSFR ...... 38 3.2.2.1. The debates around the choice of the supervisory reference metrics ...... 38 3.3. NEW MONITORING AND REPORTING REQUIREMENTS ...... 40 4. GOING FURTHER: CALIBRATING SUPERVISORY MEASURES, NOTABLY IN THE FORM OF A LIQUIDITY BUFFER ...... 41

4.1. THE NECESSITY TO DEFINE ADDITIONAL SUPERVISORY MEASURES AND THE USE OF STRESS TESTS IN THIS CONTEXT ...... 41 4.2. OUR METHODOLOGY FOR STRESS TESTING A BANK’S POSITION ON THE MID AND LONG TERM ...... 43 4.2.1. Some basic steps when stress testing and some methodological requirements...... 43 4.2.2. Steps for stress testing ...... 45 4.2.2.1. Getting the unstressed cashflow data ...... 45 4.2.2.2. The global outline of our scenarios ...... 48 4.2.3. Outcome of our stress tests and way forward ...... 50 4.2.3.1. The use of a stylised balance sheet as an input ...... 50 4.2.3.2. Detailed analysis of the stress tests ...... 52 4.2.3.3. A few methodological challenges and possible refinements in the stress testing approach ...... 54

4.2.3.4. Calibrating the counterbalancing capacity ...... 55 5. THE SPECIFIC ISSUE OF INTRA‐DAY LIQUIDITY RISK ...... 56

5.1. A SUBCATEGORY OF LIQUIDITY RISK: INTRA‐DAY LIQUIDITY RISK ...... 56 5.1.1. Introduction ...... 56 5.1.2. The sources of uncertainty for intraday liquidity risk ...... 57 5.1.3. How to manage intraday liquidity risk? Some basics ...... 58 5.2. HOW TO CALIBRATE THE LIQUIDITY BUFFER TO COVER INTRADAY LIQUIDITY RISK ...... 61 5.2.1. A framework to perform simulations: extending the Fiedler approach to intraday payments ... 61 5.2.2. How to calibrate the level of the liquidity buffer ...... 62 5.3. SOME SIMULATIONS ...... 63 5.3.1. Specification of the model ...... 63 5.3.1.1. Generating payments ...... 64 5.3.1.2. Executing payments ...... 65 5.3.1.3. Some tests on the model / sensitivity analysis ...... 67 5.4. STRESS TESTING INTRADAY LIQUIDITY RISK ...... 73 5.5. ENSURING CONSISTENCY IN THE USE OF THE LIQUIDITY BUFFER TO COVER INTRADAY LIQUIDITY RISK AND LONGER TERM RISKS 74 6. CONCLUSION ...... 74 ANNEX 1 : THE ECB SUPERVISORY MATURITY LADDER ...... 76 ANNEX 2 – MAPPING OF THE MATURITY LADDER USED FOR STRESS TESTS...... 82 ANNEX 3 ‐ MAGNITUDE OF RUNS ON FUNDING—EMPIRICAL EVIDENCE AND STRESS TEST ASSUMPTIONS ... 83 ANNEX 4 ‐ SCENARIOS USED BY THE IMF IN ITS OWN SET OF STRESS TESTS ...... 84 ANNEX 5: DETAILED RESULTS OF THE STRESS TESTS ...... 85 BIBLIOGRAPHY ...... 88

1. Defining, measuring and managing liquidity risk

1.1. How to define liquidity risk? When trying to define what would be the purpose of an adequate and efficient liquidity risk management framework, authors usually emphasize on 2 aspects:  It can be defined as the capacity to obtain cash when it is needed. This ability has a broader meaning than the simple possession of cash or assets that can be readily converted into cash. It encompasses the ability to develop and implement strategies that will help the institutions to hold these assets in due time.  It can also be considered as the ability to efficiently meet past and anticipated cash flow needs without adversely affecting daily operations. In other terms, liquidity management should give the institution the ability to maintain an equilibrium between financial inflows and outflows over time. The notion of liquidity risk derives from this: it corresponds to the situation where the institution would not be able to meet those objectives. This extends from the very short term – on the intraday horizon, it is called intraday liquidity risk ‐ to the very long term – banks in general try to manage their liquidity risk via a funding plan up to 3 years. Some authors introduce slight differences in the definition depending on whether they consider solvency risk ‐ some definitions focus on solvent firms to properly distinguish liquidity risk from solvency risk ‐, cost of obtaining liquidity ‐ funding should be obtained at a reasonable cost, but this introduces an element of subjectivity ‐ and immediacy ‐timing being important. In particular, liquidity risk should be distinguished from solvency risk and from liquidity induced value risk, even if there are interactions between those notions:  Solvency risk corresponds to the risk that the value risks of the institution outweigh its capital. In other words, the institution may be exposed to losses or to an increase of its risks that could jeopardize the level of its solvency ratio. This may become critical if the institution does not meet any more its regulatory capital requirements and/or if this creates mistrust for investors, creditors or depositors. The institution may then be obliged to take recovery measures or even to enter into resolution.  Liquidity induced‐value risk corresponds to the risk that a liquidity crisis would have an impact on the valuation of the institution’s assets, or on the rates at which it can fund itself, with a final impact on its yearly results. It can be seen as a combination of illiquidity risk ‐ when funding rates rise and reduce the expected net interest income of the institution ‐ and counterparty risk ‐ when the rates of the institution’s investments decrease due to its inability to find appropriate counterparties. Liquidity risk is usually considered as a secondary risk or a consequential risk. In fact, it is often observed that liquidity risk materialises only if other types of risks have already become critical for the institution. For example, the institution may have difficulties to fund itself after booking huge losses on its portfolio of loans. During the 2008 financial crisis, banks had to write down a large part of their portfolios of residential mortgage backed securities: due to the uncertainty about the amount of those potential losses and the lack of transparency of the various stakeholders, financial institutions became reluctant to fund their peers, up to a point where money markets were almost shut down.

Nevertheless, sufficient liquidity can be the most decisive factor in an institution’s ability to survive a crisis (it is often said that “liquidity buys time”). Liquidity can also be a key to success in a non‐crisis situation: during a period of high loan demand, a relatively liquid institution has a strong competitive advantage because it does not have to care about liquidity. Furthermore, in the 2008 crisis, liquidity has become a primary risk. Since then, it is closely monitored by institutions as such, and supervisors consider liquidity risk as a major element when analysing the situation of the institution on a yearly basis for the purpose of setting their supervisory expectations1. To operationalise the general definition of liquidity risk that we have introduced here above, we can segment it into 3 categories:  Mismatch or structural liquidity risk. Analysing the various items on the balance sheet of the institution and the corresponding cash flows, it may emerge that for given time horizons inflows may not be sufficient to cover outflows. This may derive from both contractually and behaviour driven cash flows. In this case, liquidity risk is due to the current structure of the institution's balance sheet.  Contingency liquidity risk. There is a risk that future events will require from the institution significantly larger amounts of cash than initially expected. In other terms, there is a risk that the institution may not have sufficient funds to meet sudden and unexpected short term obligations. This may happen either in the case of an institution ‐specific or of a systemic crisis.  Market liquidity risk. The institution may be unable to sell assets at or near the fair value. As the institution may have included these assets as possible liquidity sources in case of need, namely in its buffer of liquid assets, this may expose it to liquidity shortages. This type of situation needs to be anticipated, for example via conservative haircuts when measuring the value of the liquid buffers (see hereunder). The importance of those three components, as well as their interactions, may vary depending on the environment and on circumstances. In particular, they are subject to variations arising from either the severity or the duration of the crisis, in case one is experienced. One should also take into account the fact that liquidity risk may also stem from outsider’s uncertainty about the institution’s liquidity situation: liquidity risk does not always result from a reasonable and documented assessment of the situation by market participants; on the contrary, subjectivity plays a major role in this area.

1.2. Liquidity risk for insurance companies We have defined liquidity risk in general terms for all types of institutions with a focus on financial companies. Nevertheless, the financial crisis has shown that this is more a challenge for banks than for insurance companies, for several reasons. Customer liabilities are much less liquid for insurance companies and can be managed and insurers have also traditionally always held large buffers of liquid assets to meet their potential liquidity demands. Banks play a major role in financial intermediation which involves the transformation of short term liabilities into long term assets, they also face a higher risk of contagion.

1 In the context of the yearly supervisory review and examination process

The financial crisis has changed perspectives: banks are now submitted to stricter constraints as regards liquidity, insurers are seen more as liquidity providers than in the past. This may lead them to take more aggressive strategies as regards liquidity, being also encouraged by the low interest rates environment to search for additional asset yield return from less liquid assets with higher yield. The boards of insurance companies are also more sensitive to the costs of useless liquidity buffers, and support the implementation of more active liquidity management approaches. Practically, the recent years have provided some examples of liquidity crises experienced by insurance companies, merely in the life insurance branch. In those cases, policy holders have lost confidence in the company’s ability to guarantee interest rates and have surrendered the corresponding contracts2. Above a given amount of contracts surrendered, insurance companies were left without means of making the payments due, in particular when the assets backing the policies were not liquid in the short term. Some of them had to resort to costly short term loans that have proven difficult to roll‐over. Alternatively, insurance companies may face liquidity problems when having to pay out for large indemnity claims, when facing operational problems in collecting premiums or when having to honour margin calls on derivatives. Reinsurance may additionally generate a residual liquidity risk with delays in payment by the reinsurer. At this stage, solvency II mainly considers liquidity risk under pillar II, and as a consequence of market liquidity risk. Liquidity risk for insurance companies shall nevertheless not be reduced to it; they should be aware that they are exposed to all the aspects of liquidity risk, even if to a lower extent than banks. The current regulatory framework requires also insurance companies to have contingency plans, stress tests an liquidity management tools in place (CP19 of EIOPA). In the rest of this thesis, we are going to take banks as the main object of the analysis, and will refer mainly to them; the developments can nevertheless provide also relevant insights for insurance companies.

1.3. How to manage liquidity risk?

1.3.1. Standards for managing liquidity risk As a first priority, the institution, and in particular the bank needs to be able to cover the net cumulative cash outflow over a given time horizon with adequate inflows. For this, it needs to generate cash flows and at least to be able to do so in case the need arises. This entails 3 main objectives, or 3 segments:  daily management of cash flows (including management of intraday liquidity risk, see hereunder). This is the most operational aspect of liquidity risk management: the bank shall be able to influence the scheduling of future inflows and outflows to possess enough cash to meet its obligations in the very short term.  medium term management of business and operations. This corresponds to the management of structural liquidity, as defined previously.  crisis management in case of stress/disaster event: the bank shall be able to fund itself in case of a crisis via contingency funding, as defined previously.

2 This was experienced by life insurance company Equitable Life when it received an adverse legal ruling by the House of Lords on its guaranteed annuity liabilities in 2001.

To reach these objectives, the bank needs to dispose of a set of tools that should be there before any crisis emerges. As a common standard for managing risk, regulators have identified the following tools that are usually developed by banks. The list hereunder should be considered as a standard for liquidity risk management:  Banks shall be able to forecast and analyse future liquidity gaps, based on a projection of future cash flows. This projection may include behavioural adjustments and therefore some modelling. This type of analysis should be done per currency, per region or per liquidity sub‐ group if any exists in the bank.  They shall develop a contingency funding plan as described earlier.  Banks should develop stress and scenario analysis. We will elaborate on this later, but this requires capturing the main characteristics of the balance sheet, so as to group items based on their patterns in case of a crisis, to assess the shocks that those items may experience, to simulate their impact on the balance sheet and to analyse the outcome of the various scenarios.  The banks’ risk management should identify the main metrics to monitor as regards liquidity risk, place limits on them so as to define a consistent limit system. It should also define an a reporting process as well as an escalation process in case of any breach.  Banks should be able to analyse the diversification of their funding sources. They should also define diversification targets, as excessive concentration can turn into a major weakness. Diversification can be required as regards the various types of instruments (deposits, loans, etc), the types of counterparts (retail, corporate, sovereign, etc), or even regions, sectors or countries.  Banks should be able to evaluate and allocate the internal price of liquidity in the form of a fund transfer pricing system. The various business lines and business units should bear the costs associated with liquidity risk they generate for the bank. This may have a major impact on the allocation of costs and revenues between various business units and business lines as well as on the steering of the bank’s activities.  Banks should put in place an independent oversight of liquidity risk by a liquidity risk control unit that regularly reports on the liquidity status to senior management. Usual requirements concerning the quality, comprehensiveness, timeliness and appropriateness of internal risk reporting apply here. The liquidity risk control function may as well be in charge of validating the behavioural models developed to forecast future payments.  The liquidity risk function shall develop in cooperation with the various business units a liquidity policy that documents methodology, processes and responsibilities under normal but also stressed circumstances. Those documents should be endorsed at the highest level in the bank and applied consistently in the full group.  Last but not least, the bank should dispose of an adequate counterbalancing capacity. We will elaborate on this later. As mentioned in some of the items listed above, measuring liquidity may require both simple and sophisticated tools, including some modelling. A thorough understanding of market dynamics and product know‐how is required though, whatever the complexity of the bank business and of the behaviour of the clients.

1.3.2. Different strategies to reduce structural liquidity sources and contingent liquidity risk In its management of liquidity risk, the bank may take some actions to increase structural liquidity. The purpose here for the institution is to hold sufficient liquidity to meet its liquidity needs in the normal course of business. For this purpose, banks shall develop strategies which stabilise funding and facilitate the access to liquidity in case of need. We listed hereunder examples of actions that can be taken by a bank to improve structural liquidity:  As regards assets, banks should hold portfolios of liquid assets that can be pledged or sold in case of a need, namely a buffer of liquid assets. An articulated strategy for managing pledging can help, the bank shall for example pledge preferably the less liquid assets first, so as to keep the other assets available for more distressed conditions. Another option for the bank is to increase its holding of securities that provide cash flow (e.g. securitisations where there are also intermediary principal payments).  Banks may also implement various strategies to increase their liabilities that also represent liquidity sources: o Deposits – banks can increase cross‐selling and manage their relationship with their customers to reduce their tendency to transfer their assets to competitors. For the same purpose, they can offer relatively attractive interest rates for insured and local deposits. Those various actions will increase the stickiness of the assets. We will elaborate on this later. o Wholesale funding – banks should test their borrowing lines regularly, maintain close relationships with fund providers, rely as much as possible on the most stable funding providers, diversify their types and geographic locations and manage the term structure of their funding sources (ensuring as much as much as possible access to longer funding sources). Banks need to dispose of a toolbox to face various types of future conditions, but diversifying liquidity sources is not always the best strategy. For example, it may not always be useful to diversify the types of instruments: counterparties define global limits on the various counterparties whatever the type of instrument, and exposures on the various instruments may therefore be fungible. The behaviour of fund providers is sometimes very closely correlated, reputation playing in particular a major role in determining their behaviour. It may be more relevant as regards diversification to manage the term structure of liabilities. Prudential liquidity cushions are also a very relevant source of liquidity as their usage is more at the discretion of the bank. So as to mitigate liquidity risk in case of a crisis, i.e. contingent liquidity, banks may implement multiple strategies, each of which ordinarily generating a cost. Those strategies may rely on one of the following options:  Banks may shorten asset maturities so as to rely less on long term funding.  They may dispose of liquid assets or repo them. Bank can also more carefully select the assets they hold so as to improve their average liquidity.  In the short term, banks may increase short term borrowings or lengthen the maturities of their liabilities.  They may issue more equity as equity in itself is a liquidity source.  They may reduce contingent commitments that are a major cause of uncertainty when liquidity sources drain and market participants try to leverage on all possibilities available to

reduce their own risk.  They may try to obtain liquidity protection in the form of a guaranty provided by a 3rd person. The purpose there is to hold enough liquidity to buy time in the event of a crisis. All those strategies are nevertheless associated with a cost; the issue is therefore to constantly balance the benefits of the mitigating actions with their drawbacks. Liquidity risk management shall not come at the cost of profitability or solvency. It should be noted that costs are not static and that they may depend on the exogenous economic conditions.

1.3.3. The crucial role played by the counterbalancing capacity (CBC) and liquid buffers

1.3.3.1. The counterbalancing capacity: from the short term horizon to the long term horizon Capital is not considered as a strong risk cushion under conditions that are stressful for liquidity or in case of a liquidity shortage. It is not held in cash, and is invested in various instruments that may not be liquid at all. The “capital cushion” is rather a protection against insolvency risk, i.e. the risk that the bank may not be able to honour its commitments towards its various creditors and in particular its depositors. Thus, the real protection for a bank is to hold a portfolio of liquid assets that can be disposed of in case of need: to assess this, an analyst should go through the various balance sheet items and assess to which extent they can be converted into cash in case of a crisis. Selling or repoing assets is only one of the actions that a bank can take to remain liquid. On a longer time horizon, much more possibilities are open: they were discussed in the previous title. Moreover, the possibility to use one strategy or another depends on circumstances. In particular, some liquidity sources are more available in some circumstances than in others, they come at a different cost depending on market conditions. Therefore, we will adopt a definition of the counterbalancing capacity that will be broader that the sole ownership of liquid assets: the counterbalancing capacity may be defined as a plan to hold or have access to excess liquidity over and above a business as usual scenario over the short, medium and long term time horizons in response to stress scenarios, as well as a plan for further liquidity generation capacities, whether through tapping additional funding sources, making funding adjustments to the business, or through other more fundamental measures. The counterbalancing capacity is above all a strategy to be implemented in the short, middle and long term to help the bank honour its payment obligations. Holding a liquid buffer, as defined hereafter, is only a realisation in the very short term of this strategy. In addition, one should also acknowledge the fact that even the counterbalancing capacity incorporates a stochastic component: indeed, the bank needs to adjust its strategy based on the evolution of markets. This means that when forecasting the liquidity profile of the bank, one should ideally also consider the strategy taken by the bank as non‐deterministic. The longer the time horizon, the larger should be the set of actions that may be taken by the bank.

1.3.3.2. The liquid buffer The liquid buffer determines the very short end of the counterbalancing capacity. Holding a buffer is a direct insurance against potential shortages in liquidity. It represents available resources designed at covering the additional need for liquidity that may arise over a defined short period of time under

10 stress conditions. Under a short term horizon, converting part or the full amount of its portfolio of liquid assets into cash may even be one of the only options available for institutions. The quality of the insurance provided by the liquid buffer is determined by a combination of the size of the buffer and the quality of the assets it comprises. The liquidity buffer may be composed of the following assets:  Cash readily available at the central bank, already pledged or not, that will be necessary for the bank to be granted a liquidity line.  Asset maintained in ancillary systems3. Those can be bonds, but also trade receivables. Ancillary systems can also grant liquidity lines to credit institutions.  Assets held on the balance sheet but that can be made liquid if necessary. This includes marketable assets, but the bank may also securitise non marketable assets. For example, a bank may get liquidity from a portfolio of loans via issuing collateralised loan obligations (CLOs), it can proceed similarly with residential or commercial mortgages. Even if those are not sold to external investors, they may, under some circumstances, be pledged at the central bank to get access to liquidity. In a nutshell, there are two ways of using the liquid buffer:  Balance sheet expansion (repos). This is the most common use of the liquidity buffer. The bank may also pledge unencumbered assets to secure loans. Repos are a quite flexible tool, there exists a liquid market on which they are traded for a large set of securities, and they come at a cost that may be lower than the one associated with the pure sale of assets.  Balance sheet reduction (selling or securitizing assets). Indeed, the bank may simply sell some of its liquid assets. Practitioners tend to distinguish two views of the liquidity buffer: either they focus on its “pledgeability” at the central bank, or they consider other options available that are considered for the computation of the liquidity coverage ratio (LCR) ‐ using other pledging possibilities, selling the assets, etc. In the latter case, they will usually refer to the liquid buffer as being a buffer of high quality liquid assets (HQLA), this notion being defined in the European regulation. We should mention that maintaining and making use of a buffer of liquid assets comes at a cost that can be affected by market conditions: the buffer needs to be refinanced, repo transactions as well as the sale of assets have a cost. If markets are completely disrupted, it may simply be that the bank will be unable to sell its assets, or will be able to do it with taking a significant mark‐down. In this context, one can develop three alternative views of the buffer of liquid assets:  Under a “business as usual” view, the buffer is estimated as the total amount of readily available funds that can be used to offset the “business as usual” net funding gap.  The “planned stress” view will focus on the need to be able to offset the Planned stress net funding gap. It will lead the bank to add planned additional funds to those held under the “business as usual” scenario.  Under the “protracted stress” view, the bank will add other fund generation possibilities through contingency funding plan to offset incremental protracted stress net funding gap.

3 Ancillary system: a system in which payments or securities are exchanged and/or cleared. Meanwhile, the ensuing monetary obligations are settled in another system.

Moving from one view to the others, the bank will tend to consider a longer time horizon, and also a larger set of strategies to be implemented. It will move from the strict and restrictive consideration of the buffer of liquid assets to the broader consideration of the counterbalancing capacity. In addition, it shall be noted that liquidity risk is asymmetrical. Having large liquidity reserves is not beneficial and can be costly; too little liquidity can lead to a bank failure. We will refer here again to the delicate balance that always needs to be stroke between perfectly hedging and covering risks and maintaining the profitability of the bank. It goes without saying that the calibration of the liquid buffer as a reserve to cover illiquidity risk is essential. In this context, there are four common issues with liquid assets that need to be taken into consideration when calibrating the liquid buffer:  The risk of a lack of asset marketability. This risk materialises if it becomes more difficult to sell assets that are in principle considered as marketable. It may be discerned via the liquidity premium, i.e. the bid‐ask spread, and quite naturally, asset marketability can change through time and needs to be carefully monitored by the bank. The liquidity of an asset may be determined by multiple factors: an asset is liquid if it is traded on an active and sizable market, if the corresponding market benefits from the presence of committed market makers, if market concentration is low, if credit risk associated with the asset is low, if the asset is easy to value, if it presents a low correlation with risky assets, or if it is listed on a developed and recognised market. An asset can be considered as being very marketable if participants can execute large transactions as needed and if there is no meaningful difference between the realizable and carrying value of the asset.  Excessive concentrations. A bank is exposed to this kind of risk if it holds a position in an asset that is large as compared to the corresponding daily turnover. If so, it may experience some difference between the average execution price and the ex‐ante mid‐market price. Therefore, banks should always compare the actual size position to the depth of the corresponding market.  Misvalued assets. Assets may be misvalued due to their excessive size, to their structure being too complex, due to errors in modelling or haircut assumptions or if their valuation is based on dynamic parameters that fluctuate highly with market conditions or that rely on assumptions that are subjective. Stress events also tend to reveal unexpected interrelationships that may not have been incorporated when valuing the asset. The firm may therefore be assured that it will be able to pledge or sell the assets, but the price at which it will be able to do it remains critical. Asset liquidity is also impacted by transaction costs that may evolve with time and circumstances.  Lack of unencumbered assets. An asset is defined as encumbered asset by the EBA Guidelines on the disclosure of encumbered and unencumbered assets4 “if it has been pledged or if it is subject to any form of arrangement to secure, collateralise or credit enhance any on‐balance‐ sheet or off‐balance‐sheet transaction from which it cannot be freely withdrawn (for instance, to be pledged for funding purposes). Assets pledged that are subject to any restrictions in withdrawal, such as assets that require prior approval before withdrawal or replacement by other assets, should be considered encumbered”. Even if the bank disposes of a very large buffer of liquid assets, it shall therefore also monitor the restrictions mentioned above.

4 EBA/GL/2014/03

To conclude this list, it is worth highlighting the existence of “liquidity black holes”. Those episodes of an extreme kind have been very well described by academics: all market stakeholders give orders to sell their positions, prices evolve very rapidly and traders experience financial distress. It results that some positions may not be closed unless under very unfavourable conditions, and part of the buffer of liquid assets may be considered as useless. This type of situation, though associated with a very low probability, may cause major harm, and therefore shall be considered in the stress testing framework. To cover problems raised by the first three bullet points, the bank and the supervisor apply different levels of haircuts when computing the support provided by the liquidity buffer against liquidity risk. The haircut depends on many factors, including the nature of the asset and market conditions. A market shock may indeed lead to a reduction in the value of the buffer of liquid assets. Therefore, through the liquid buffer, there is a link between funding risk and market liquidity risk. In most banks, as well as in calculation of the regulatory liquidity coverage ratio, the determination of the haircut is based on several criteria: for example, eligibility for the ECB refinancing, size of the position, rating, issuer group (OECD, G7 or emerging market), issuer type (government, bank, corporate), listing location, currency, own position against total outstanding and degree of structuring. A few financial indicators can also be used to determine the level of the haircuts. They more or less overlap with the criteria listed here above:  Depth and standardisation of the market. Absolute market size in not in itself an indication of depth: the level of activity on the market is also important. The amount of orders in an exchange trading book shall be closely monitored.  Tightness of the market. It may be observed through bid‐offer spreads. Nevertheless, it is important to note that liquidity cannot always be measured via bid‐offer spreads: this is in particular the case for marked to model assets. Assumptions in the valuation shall be different under stressed conditions.  Resiliency & operational efficiency of the market. The market shall be able to absorb a large block of assets. This can be measured through additional measures: number of trades in an asset, monetary volume of trades in an asset, frequency of trades in an asset, turnover in an asset or number of market makers, etc. Last, but not least, credit institutions should respect some rules as regards liquid buffers. In particular:  As mentioned earlier, they should avoid holding large concentrations of particular assets, but there also should be no legal regulatory or operational impediments to using those assets.  The location and size of liquidity buffers within a banking group should adequately reflect the structure and activities of the group in order to minimize the effect of possible legal, regulatory or operational impediments to using the assets in the buffer. This is particularly sensitive for large international banks for which liquidity may be trapped in some of the locations, the bank not being always aware of it.

1.3.4. Contingency planning Contingency planning is not the main focus of this work, but we will elaborate shortly on it. It would be too costly for a bank to try to hedge oneself against all possible liquidity scenarios. But having sufficient liquidity is often a condition to survive a crisis. A major component of liquidity risk management therefore consists in being able to enhance liquidity quickly at the first signs of increased potential need. In particular, the bank shall able to identify the early stages of a crisis, and under such circumstances it shall promptly raise and manage liquidity. It is sometimes said that contingency planning represents the “bridge” between the liquidity the bank chooses to hold and the maximum it might need. It represents a protection to avoid sub‐ optimal decision making under distressed conditions. It is focussed on the tail of the distribution of scenarios that the bank may experience as regards liquidity; we will see later that this is where the notion of liquidity management takes its real value. Contingency planning can be defined as a combination of early warning procedures and pre‐ elaborated action plans that help the bank to react adequately to potential high severity/low probability scenarios. Some best practices can be highlighted as regards contingency funding plans:  Contingency funding plans need to have well‐defined triggers. Among the set of possible triggers, the following can be identified: a decline in earnings, an increase in the level of non‐ performing assets, an increase in the level of loan losses, a downgrading by a rating agency, an increase in the spread paid for uninsured deposits, borrowed funds or asset securitizations, a sudden decline in the stock price, significant asset growth or acquisition, legal, regulatory or tax changes that make borrowing less attractive, etc. There should be a graduation as regards the severity of those warnings. Up to a certain level, they may simply lead the liquidity risk control function to issue warnings for business lines and senior managers. Above certain thresholds, escalation procedures should be in place and corrective actions shall be taken immediately.  Both triggers and potential remedial actions must be defined and organised to reflect differences in conditions associated with different scenarios, and assignments for responsibility must be clear and cover all possible configurations.  Contingency funding plans need to incorporate as many remedial actions as possible. Identifying those actions is the core of contingency funding planning in itself. It is easier to figure in advance the list of actions that may be taken to fight against a liquidity shortage than to do it under stressed circumstances.  The contingency funding plan should plan in advance how both internal and external communications will be organised. The outcome of this analysis must be realistic.  Lastly, plans must be tested. To do this, the bank may try regularly to take the following actions: it may try to sell loans, to repo securities, to borrow from the central bank, to securitise assets, etc. Large banks which have more resources for managing their risks should in particular organise regular simulations that will include multiple business lines as well as senior management.

1.4. How to measure liquidity risk under normal conditions? The current paradigm to measure and monitor “regular” risks, in particular credit and market risk, relies usually on at least 3 types of tools: sensitivity measures which help analyse exposure to a large

14 variety of risk factors in a linear approach (sensitivities), synthetic measures capturing non‐linear effects like VaR, and stress tests to consider scenarios with a low probability and a high impact. As regards liquidity risk, the approach is slightly different. Risk professionals tried to apply quantitative techniques like VaR to illiquidity and to model it in a way that the result would be one number, Liquidity‐at Risk. LaR would be deducted from the distribution of various risk factors. This concept is practically unusable as regards liquidity risk: illiquidity risk cannot be expressed as value risk; it is problematic to infer the distribution of the main liquidity risk metrics from statistical observations because illiquidity risk emerges only in situations where behaviours and markets which have been stable for long periods suddenly change. Furthermore, it is impossible to estimate the probability of the bank becoming illiquid, because it would require the estimation of a huge number of variables. Many underlying liquidity variables cannot be expressed with probability distributions or there may be unexpected changes in the probability distribution; the impact of illiquidity is almost binary. Optionality is also a major issue: as regards liquidity, there are many implicit options; forecasting which ones will be exercised may be very challenging. Therefore, other types of metrics have been defined as regards liquidity risk. We will mention hereafter various approaches in this regard, in a non‐exhaustive list. Before we introduce a list of possible liquidity metrics, let’s mention that Matz has developed5 a list of attributes that would characterise a good liquidity risk metric. An adequate liquidity metric should be:  Comprehensive: it should take all assets into consideration, as well as all liabilities and off‐ balance sheet sources and uses of liquidity.  Flexible: it can show assets (loans as well as investments) as both sources and uses of liquidity. It can show liabilities as stable or volatile.  It uses prospective, not historical cash flow data.  It reflects the fact that liquidity sources and uses are scenario specific.  It reflects the temporal nature of liquidity risk. We will use this grid later in the paper to analyse the strengths and weaknesses of various liquidity metrics. Overall, we identified 4 different approaches that are used to measure liquidity risk. We ranked them hereunder mainly by their level of sophistication: some metrics are relatively simple and rely on data that necessitate less expert adjustments to be delivered, but they may miss some of the specificities of liquidity risk. Some others may be more accurate due to a finer assessment of risks, at the risk of introducing some subjectivity in their calculation.  The balance sheet liquidity analysis. It relies on the assumption that sticky assets, namely assets that will remain for long on the balance sheet shall be funded by stable liabilities, whereas liquid assets can be funded by volatile liabilities. In other words, the most unstable sources of liquidity should serve to fund assets than can be converted into cash rapidly. Conversely, the bank should use more stable funding sources for positions that may stay longer on the balance sheet. Those approaches rely usually on accounting data: they present

5 Liquidity Risk Management, Matz, Leonard M. 2001.

the advantage of being easy to compute and to rely on data that is deemed to be more reliable than other type of internal data sources. There are numerous examples of such ratios which are frequently used by banks: the most common one is the loan to deposit ratio. Banks also compare the amount of liquid assets to the total amount of liabilities, or the amount of liquid assets minus large liabilities with the total amount of assets. They may also divide the total amount of short‐term money market liabilities, those being the least stable ones with the total amount of assets. Those measures present various drawbacks.  In particular, they miss the time dimension. Indeed, they are based on a static view of the balance sheet at a given point in time without making any projection on the predictable evolutions (e.g. repayment of some assets, roll‐over of some funding sources, etc).  They do not take into account the fact that the liquidity position of a bank depends also on its financial environment. For example, the loan to deposit ratio considers in a similar manner all kind of deposits, whether sticky or not: under financial stress, this hypothesis may prove to be very inaccurate, as was observed during the 2008 financial crisis.  Relying on accounting data may create distortions between banks applying different accounting rules. Accounting segmentations may not always coincide with classifications that are relevant for liquidity risk monitoring: some loans may be securitised, some others may be reimbursed under some conditions or may be repaid soon.  Those measures also neglect most of the time off‐balance‐sheet commitments that may prove to be a major source of uncertainty in case of a liquidity crisis: for example, commitments provided by banks to securitisation vehicles were a huge liquidity drain for some banks in 2008.  The heterogeneous marketability of securities should also be taken into account.  Cash capital analysis. This approach was introduced by Moody’s. It measures the banks’ ability to fund themselves on a fully collateralized basis, assuming that access to unsecured funding has been lost. More practically, the corresponding metric is based on the gap between the collateral value of unencumbered assets (i.e. the total liquid assets, including cash, TLA) and the volume of short term interbank funding and of the non‐core part of non‐ bank deposits (i.e. the total volatile liabilities, TVL). One can also include the commitment taken by the bank to lend to some external stakeholders (Commitment to lend, CTL). Consequently, the Cash Capital Position is computed with the following equation: CCP= TLA‐TVL‐CLT The cash capital approach relies on a classification of liquidity sources and uses and of assets and liabilities that is more risk‐based than the balance sheet analysis. Nevertheless, we can still identify some drawbacks:  As much as approaches based on the analysis of the balance sheet, they miss part of the dynamics of the positions. For example, they do not take into account long term liabilities that are maturing within a short term horizon.  They also do not take into account liquidity generated by the bank’s business.

 The discount applied to marketable securities has to be carefully calibrated. Being either too low or too high it may result in an underestimation or in an overestimation of liquidity risk  This measure is also not very forward looking. Both approaches present the advantage of delivering ratios that could be convenient to benchmark institutions and compare their situation at a given point in time. It is nevertheless important to highlight that this should be done only within peer groups and if the peers are very well chosen. They are quite inadequate to compare institutions having completely different business models.  Maturity mismatch analysis / cash flow based approaches. These approaches consist in mapping cash flows to a maturity ladder and to compute net cumulative outflows, and therefore liquidity gaps for various buckets. Schematically, the net cumulative outflow can be considered as an equivalent to VaR, but with quite large differences, one of them being that the maturity mismatch is computed under a given scenario. We will provide later much more details on the assumptions and methodological choices to be taken in the context of the description of the approach developed by Robert Fiedler, and we will provide in this chapter only a quick introduction on the topic. The main objective of a prudent liquidity management framework should be to ensure that the net cumulative gap shall not become negative before a given date. Resulting from these calculations, the bank shall be able to compute the funding ratio on a given time horizon and this metric can be used for steering liquidity risk in the bank. So as to compute net cumulated outflows on a given horizon, the bank has the choice between two options: focussing on the operative maturity ladder or rather on the strategic maturity ladder. In the former approach, balance sheet items included in the operative maturity ladder belong to the treasury book: they include short term cash and derivative wholesale instruments, interbank and institutional client deposits, repurchase agreements, cross currency swaps, middle term notes, certificates of deposits, commercial papers, etc. Conversely, highly volatile assets, cash accounts and credit cards are not integrated. The strategic maturity ladder includes more elements. It is often considered that the maturity mismatch analysis is one of the best tools to capture liquidity risk in the normal course of business. Nevertheless, some of its drawbacks should be mentioned.  The liquidity gap can only be computed under given scenarios and the choice of the scenarios, which remains quite subjective, will strongly determine how liquidity risk will be monitored and steered. One should know that the chosen scenario can be as simple as a simple roll‐over of exposures or, conversely, their run‐off.  Forecasting future cash flows necessitates some modelling assumptions that may become less relevant if the financial environment changes, and in particular in a period of stress. This should be properly taken into consideration and specific models should be used in the context of stress tests.  As modelling and forecasting cash flows at a very granular level may be very demanding both in time and resources, banks may need to focus on the most relevant balance sheet items: this is where we could reiterate some of the critics formulated regarding the metrics described earlier.

The table hereunder summarises an analysis of the approaches presented up to now with the criteria developed by Leonard Matz that were listed here above:

Balance sheet liquidity Cash capital analysis Maturity mismatch analysis analysis

The metric shall be No: most of those metrics No: the metric focusses on Yes/No: it is the case if the comprehensive focus on a limited number of the unencumbered liquid modelling of the balance balance sheet items. assets and on the most sheet and off balance sheet volatile part of the funding items is very granular. sources. Nevertheless, with the commitment to lend, some off balance sheet items are considered.

The metric shall be No: most of the metrics No: items taken into Yes: when projecting cash flexible based on a balance sheet consideration have a univocal flows, the bank can take into analysis view items as being impact on liquidity, either account the fact that most either a liquidity source or a being a liquidity source or balance sheet items may liquidity use one of its uses have an ambiguous impact on their liquidity

The metric shall be Yes/no: the metric does not Yes/no: the institution may Yes/no: some scenarios used prospective rely on a calibration based on apply haircuts or for the computation can be past observations, but multiplicators to some of the forward looking, others more neither on forward looking items used for the backward looking. assumptions computation. Those can be based on backward looking or forward looking assumptions

The metric shall be No No Yes: there is only one scenario specific scenario per analysis, but different scenarios can be applied. This may be a drawback, as the outcome may be very scenario‐ dependent as we mentioned earlier.

The metric shall reflect No No Yes: the approach may take the temporal nature of into account any time liquidity risk horizon.

 Hybrid approaches These approaches combine elements of the cash flow analysis and of the more static approaches described before. The underlying assumption is that the bank may be exposed to unexpected cash in‐ and outflows, and that those may deviate significantly in their timing or magnitude from what is usually observed. The bank tries to match cash expected and unexpected outflows in each time bucket against a combination of contractual cash inflows plus inflows that can be generated through the sale of assets, repurchase agreements or other secured borrowing. Most liquid assets are counted in the shortest time buckets, less liquid assets are counted in longer time buckets. Those metrics can be computed on various time horizons. They present the advantage that they can easily be standardised and therefore facilitate comparison between various banks. For this reason, they have become part of the supervisory toolkit with the liquidity coverage ratio. LCR, that will be discussed later, is indeed a mixture of the balance sheet view and of the cash flow view.

Those approaches can be assimilated to a kind of standardised stress‐testing and, more particularly, LCR. Nevertheless, those metrics should be complemented with a proper and diversified set of stress tests. We will discuss this in more detail hereunder.

2. A conceptual framework to analyse the maturity mismatch

2.1. The approach defined by Robert Fiedler

2.1.1. Description of the conceptual framework

2.1.1.1. Introduction of a few basic concepts We have explained earlier that the maturity mismatch analysis is among the most appropriate approaches to measure and monitor liquidity risk. It necessitates the computation of future “cash‐ flows” so as to deduct from those a future “cash‐flow inventory”, which is namely the amount that the bank will hold in the future on its central bank account (its nostro account). To present how the cash flows and the future cash inventory can be calculated, we need to introduce a few basic concepts. Please note that the definition given here to some of those concepts may differ significantly from what is usually understood under the accounting approach.  Assets. Assets are taken in a very broad sense: they are constituted by all balance sheet, either being assets or liabilities according to accounting standards, and off balance sheet positions. Deposits, swaps, bonds and shares are the most simple examples of assets; credit lines, derivatives, guaranties are also considered as assets in our approach. Those assets present various characteristics: for example, some assets are marketable or pledgeable, some are not. In our framework, they will be grouped into “asset units”, i.e. congeneric types of transactions, if they have comparable behaviours in a given scenario (see later the notion of scenario). Asset units should be disjunct, but together they should cover the full balance sheet. For example, we may group all marketable securities into one category, group deposits into another one, or consider that retail deposits should be distinguished from corporate deposits, etc… The amount held as a deposit on the nostro account is a specific type of asset which plays the most important role as regards liquidity risk. Banks should whatever the circumstances maintain this amount positive. To do this, they may nevertheless benefit from liquidity lines provided by the central bank. Assets can be exchanged against each other, they are fungible: for example, selling a bond may increase the amount held the nostro account. It is possible to hold an inventory of each asset type and to forecast their evolution through time. We will denote the forecasted stock of asset i at time t.  Financial transactions are operations that result in the change in the inventory of at least one type of asset. They can result from the exchange of assets, but not only. For example, buying, or pledging an security will be considered as a financial transaction that will increase or decrease the marketable security inventory and correlatively decrease or increase the cash inventory. When a client withdraws deposits from a given bank account in the form of banknotes, it reduces the amount of retail deposits that the bank disposes of as well as it amount of banknotes. A transaction can more precisely be defined as any kind of operation

deriving from an agreement between the bank and other parties that will result in the change of the inventory of at least one asset type.  A change in the cash inventory, i.e. the amount held on the nostro account is a payment. Transactions that are relevant for liquidity monitoring are those that result in at least one payment. Nevertheless, all payments do not stem from financial transactions, some are simply generated by assets that are already on the balance sheet of the bank. Indeed, assets generate payments in themselves: for example, a bond generates coupons, a sight or a fixed deposit may generate interest for the bank, etc.  A liquidity option is a specific type of option that, if exercised, will trigger a financial transaction resulting in a payment. We will focus here on options that may have a significant impact on the liquidity position of the bank. We can provide here a more detailled classification of liquidity options:

o Some liquidity options are explicit, some are not. The archetypical type of an explicit liquidity option consists in the right to draw on a credit facility given to a client. As an example of an implicit liquidity option, we can mention the right for clients who hold savings deposits to withdraw their money and to move it to a deposit account for example. The bank itself disposes of the option to change the interest rate of the deposit. There exist even more implicit liquidity options: For example, the bank may decide to grow its business, and therefore grant new loans. Breaches in scheduled transaction can be simulated as the exercise of an option that generates exactly the opposite transaction.

o Some liquidity options are enforceable by the bank or the client, some are not; conversely, some are rejectable by the bank, some are not. The bank benefits for example of the following non‐rejectable liquidity options: the sale of assets from the balance sheet, the shortening of the maturity of assets (loans given), the extension of the maturity of existing liabilities, the acquisition of new unsecured liabilities, the acquisition of new secured liabilities (repo). One aspect in the optionality is that the bank, or the client, may also have the freedom to decide when it will be exercised. This aspect is quite important for the management of intraday liquidity risk. It is crucial for the bank to have the right or the ability to postpone some payments. The bank may be short or long in the liquidity option. If short, the bank must accept the counterparty’s decision to exercise the option: for example, it shall let its clients withdraw their savings deposits or call an additional loan tranche if it results from a contractual agreement. If it is long in a liquidity option: the bank itself can exercise the option. For example, it can decide to draw on a liquidity facility or sell a bond against cash, etc. It is crucial for a bank to be able to hold a detailed inventory of the liquidity options that are the most relevant for liquidity risk management, and to be aware of the exact circumstances under which they can, or may be exercised. This may be extremely challenging. For example, some banks underestimated dramatically before the crisis the impact of the liquidity lines that they had provided to special purpose vehicles in the context of securitisation transaction they had sponsored. On this basis, it is possible to define different stochastic variables:  Future payments. Payments have been defined earlier; they can be considered as realisations of a stochastic process. Cash flows are the current forecast of future payments. They are based on the current asset and liquidity option inventory. We will note those ,, i

corresponding to a given asset and t to the time where the payment will be realised.

 Future asset flows, denoted as , represent all moves that will affect the asset flow inventory for asset i at time t. A future asset flow may be connected to a future payment, but not necessarily. As said previously, an asset may for example be exchanged against another, the cash inventory of the bank not being affected.

 Future unused option flows , are those flows that will have an impact on the inventory of available unused options. They are measured at time t for option i. It is very difficult to precisely hold an inventory of unused liquidity options, as their number is endless. The final purpose of the bank in the Fiedler approach is to forecast future payments. In this regard, it is necessary and sufficient to forecast not only future financial transactions that will result in payments, but also payments that result from the existing stock of assets. Some assumptions will be relied upon in the following paragraphs:  inflows and outflows planned on the same day can be netted  short/long positions are funded respectively placed until the next payment day  interest effects are neglected

2.1.1.2. Characterisation of cash flows based on their uncertainty Cash flows present various characteristics that we will detail hereafter. For example, there are deterministic and volatile cash flows: deterministic cash flows are those that are certain, both in their existence and amount; volatile cash flows are uncertain, on one of those aspects, or on both. Payments can also be univoqual (they are determined by a contractual schedule), they can depend on future values of market variables, they can depend on decisions of the counterparty or the bank to execute options. One should take into account 2 components when forecasting cash flows: • If the cash flow does not result from the exercise of a liquidity option, it is usually qualified as contractual, i.e. it results from the execution of already existing contractual clauses. Contractual cash flows are not always deterministic: some uncertainty may remain as regards their amount. o Fully deterministic cash flows will be denoted . The counterparty and the bank are financially and operationally able and willing to execute all cash flows, as they have been agreed by contract. This is the part that can be easily forecasted, whatever the scenario. Nevertheless, there is some uncertainty, on the fact that the payment will be executed as scheduled, but we will neglect this effect at this stage. o Part of the contractual cash flows are probabilistic, mainly because they are a function of market parameters (e.g. equity linked payments, floating leg of a swap). Once the value of the parameter is known, the value of the cash flow itself is known as well. Such payments may be forecasted as well, if we are able to forecast the future level of the underlying market parameters. There will be an error in the forecast, but the forecasting approach can be subject to the usual back‐testing methods and the expected quality of the forecasting process may be known in advance. As regards interest rates, it is worth noting that using the forward rates curve may not always be the best option as it mainly reflects the anticipations of markets: it may be much more adequate to define scenarios that will be tailor‐made for the bank.  Conversely, contingent, or hypothetical cash flows result from the exercise of liquidity options

by the bank or by one of its counterparts. They stem from future transactions that do not exist yet. Therefore, they introduce some dynamic uncertainty in the modelling. Some transactions may be anticipated but still uncertain: for example, it will be the case if the bank is structuring operations without having completely finalised them yet. This is the non‐ deterministic part of the cash flows and it will denoted in the future Contingent cash flows can either be endogenous or exogenous:  Endogenous cash flows are derived from existing transactions. They can be ordered in 3 groups. Some of them will come as the replacement of an existing transactions: it will be the case for example with the renewal of a loan or of a deposit. Some of them will be conditional: a client may draw a certain amount of liquidity under an existing facility. A last category is represented by unenforceable transactions: the client may for example be unable of client to pay back a loan as scheduled.  Other cash‐flows are fully exogenous and cannot be derived directly from the current position of the bank. It may result for example from the bank’s choice to do some new business in the future, or from the acquisition of new clients. The table hereunder aims at sorting out cash flow depending on which of its aspects may be stochastic6:

Cash flow amount

Deterministic Stochastic

Fixes rate term loans and mortgages Variation margins Cash/repos/collateralized lending European options

Deterministic Term deposits Non‐fixed coupons Fixed coupon payments Dividends timing

Notional exchange from CCS Traveller’s cheques Revolving loans flow Callable bonds Current accounts

Cash Stochastic Loan with flexible amortisation schedule Sight and saving deposits Marketable assets American options

2.1.1.3. Defining the forward looking exposure As mentioned earlier, banks aim at forecasting future cash flows under various assumptions, i.e. scenarios (we will provide a definition later) so as to be able to reach their targets as regards the amount they hold on their nostro account at any moment. When cumulating all expected transactions, it is possible to compute an overall expected cash flow which corresponds to the sum of all positive and negative expected cash flows from day one to the whole time horizon ; it permits to predict how forthcoming payments will change today’s nostro balance in the future. It depends on time, i.e. (ECF = Expected cash flows) The forecast of the cash inventory, also denominated the forward looking exposure for time t, corresponds to the sum of all previous expected cash flows: ∑ (FLE = forward looking exposure)

6 See Vento Bank liquidity risk management and supervision: which lessons from recent market turmoil

We can draw here a distinction between positive cashflows (inflows, denoted ) and negative cashflows (outflows, denoted ). If we group cashflows based on their incoming or outgoing nature, we have: We also can rely on the distinction between deterministic and non‐deterministic cash flows. We have then:

A few observations need to be highlighted at this stage:

 A bank shall calculate a separate FLE for each currency. Let’s denote , the forward looking exposure at time for currency .  It is possible to group assets and corresponding payments into portfolios (e.g. retail deposits, liquid bonds portfolio, etc). Similarly, the forward looking exposure can be split into different portfolios. For example, the cash inventory can be split for different portfolios of transactions: in particular a different cash flow inventory can be held for each trading desk, or for the various business lines, etc.  The bank can take a discretised version of the time scale, namely it can define future time buckets to simplify the production, the analysis and the monitoring of expected cash flows. It is essential for this segmentation to be granular enough, so that the necessary aggregation will not result in neglecting future liquidity gaps (to be defined more in detail later). Similarly to what has been described previously, it is possible to compute the forward asset inventory () and theoretically the forward unused option inventory (), in the latter case with big reservations as some liquidity options may be very difficult to identify. Options shall also be grouped by similar types (and this may require a quite granular segmentation), as well as the assets (bonds, shares, etc). To compute the forward looking exposure, it seems absolutely necessary to compute at least the forward asset inventory.

2.1.1.4. The main aim of liquidity management: ensure a possible excess of liquidity at any time What determines the bank’s capacity to compensate a negative liquidity forecast is the fact that it holds a large enough counterbalancing capacity. If we use the terminology that we defined previously, further to being a strategy, the CBC consists in both the forward asset inventory for those assets and all unused options that may be used to generate liquidity. The CBC is defined under various scenarios; a part of those are in the hands of the bank. The bank should manage its liquidity so as to ensure at any time the following inequality: 0 Where FLE(t) is the forward looking exposure and CBC(t) the counterbalancing capacity at time t. The sum of the forward looking exposure and of the counterbalancing capacity is indeed a measure of the bank’s distance to illiquidity. Thus, the survival period, being alternatively denominated as the

23 time horizon, corresponds to the period of time where this sum remains positive. If, for one day, this inequality does not hold true, the bank becomes illiquid. So as to be able to react to a broader range of circumstances, the bank should take into account a full set of scenarios (see hereunder). Once the scenarios have been agreed on internally, risk managers should simulate whether the bank can generate “just enough cash” to balance its negative nostro account. The FLE being computed on the whole balance sheet, it includes necessarily cash flows stemming from the buffer of liquid assets. We have said earlier that selling this buffer is the main option the bank disposes of in the very short term. The CBC and the FLE are very intricated: changes in the CBC influence deeply the FLE. Computing the CBC is a more sophisticated approach than simply computing the liquidity buffer. The buffer concept does not incorporate a term structure and does not reflect the dynamics of a changing balance sheet. As regards the CBC, we will restrict ourselves for technical reasons to the modelling of transactions being securities related: buy and sell, sell and buy back, buy and sell back, repo and reverse repo, security lending and security borrowing, etc. If we distinguish between the different currencies as we did earlier, the institution shall respect the inequality at global level and in each of the currencies. Therefore, we should have: 0 with ∑ , where i is the number of currencies that the institution holds and

∑ , . We should also have

, , 0 in each of the currencies. One should notice that among its strategies, the bank may convert assets held in one currency into another currency. This transaction may have an impact on both the expected cashflows and the value of the counterbalancing capacity. Going back to the case where there is only one currency, the value of the counterbalancing capacity at future time can only be forecasted at time . The counterbalancing capacity is a forecast at time of the amount of cash available at time t (C), plus the expected amount of secured (S) and unsecured funding (U), plus the amount of assets that can be sold (A). In other terms:

, , , , , The institution will have to compute the forecasted value of each of those assets. As regards cash, the main issue will be to forecast the evolution of the corresponding amount and no haircut is applied for such a type of asset. We will disregard the amount resulting from expected cashflows, which is considered in the forward looking exposure. As regards other types of assets, let’s suppose that the bank has grouped them into N categories, each of which being associated with a corresponding haircut . As a rule, institutions do not apply different haircuts for secured funding and the possible sale of assets: therefore, we will not distinguish secured and unsecured funding in our calculation. The haircut corresponds to the possible gap between the booking value of the asset and its effective value for liquidity purposes (time to sell the asset, haircut for repos). In each of the N categories, there are M types of assets. The value of each type of asset is computed at time for time t. It is noted ,. Therefore we have:

, , , We should also include in the counterbalancing capacity the capacity for the bank to get unsecured funding, but we will deliberately neglect it, as this is a highly unpredictable aggregate.

If t is close to (typically, one day to 1 month), this equation can be simplified. We may incorporate the possible loss in value of the assets into the haircuts, and the above equation gets simplified into:

2.1.1.5. Defining scenarios and strategies to compute the FLE The FLE can only be computed if we use scenarios to simulate various predictions. A scenario is the combination of various elements:  The future state of the economy. For example, there may be a development of real estate in the given economy, that will result in the granting of a higher amount of residential mortgages  Assumptions on various financial variables, e.g. interest rates. They may result in the execution of options the bank is not long of; for example clients may do some arbitrages on the type of assets they hold (e.g. replace term deposits with sight deposits if interest rates seem too low on the possible horizon of term deposits)  The forecast of how the bank is going to use long options it disposes of to pursue policies (defined by targets, e.g. improve the quality of the portfolio, diversify the CBC, etc). It is also possible to specify counter‐scenarios which simulate the reaction of the bank to a specific scenario. In risk management, the expression “scenario” is often used in the sense of an alternate possibility which relates to a “base case” that is more or less assumption free. In liquidity risk, it is very problematic to define a base case. Even the simplest forecast entails a variety of assumptions and thus can be seen as a scenario rather than a “base case” liquidity forecast. In the end, there are no “known” future cash flows. An unlikely scenario can be as useful as a likely scenario. Scenarios can model passive or active future behaviour of the bank.

2.1.2. Main liquidity drivers to be taken into consideration when modelling future cash flows It would practically not be feasible to make assumptions and forecasts on the full balance sheet and therefore risk managers need to focus on those assets which have the most significant impact on liquidity risk. The following criteria should in particular be considered when deciding which assets to focus on:  One should in particular consider the most traditional sources and uses of funding for the bank: deposits, wholesale funding, loans, etc. They should explain the main evolutions of the liquidity position of the bank in particular under “normal” circumstances.  Volatility should also be factored in. This concerns in particular assets whose amounts may vary considerably in case of a liquidity crisis and therefore have a significant impact on

liquidity. The selection shall be based there on experience in past crises. After the 2008 crisis, banks should for example consider liquidity lines provided to SPVs more than they did before. We have identified hereunder a list of those assets, based on indications given in particular in the literature on the topic. We will group them hereafter in asset categories. They can be either sources of uses of liquidity.  Unsecured funding is often considered as being one of the most material liquidity sources when modelling liquidity risk because it is highly volatile and can drain very rapidly in case of a crisis, because some banks may highly rely on it, and because reliance on such funding may provide an ambiguous picture of the situation of the bank. Indeed, if a bank is able to raise high amounts of unsecured funding, it also means that it still benefits from the trust of investors. In the medium/long term, these liquidity sources are medium term notes and euronote facilities, long term bonds, loans, and in the short term commercial papers or short term bank facilities.  Secured funding is a more secondary source of risk because it is much more stable. It may nevertheless depend a lot on the quality of the underlying asset and therefore in the ability of the bank to keep an attractive portfolio of pledgeable assets. It may experience problems if counterparties stop rolling over their positions and if the bank loses access to the market on both secured and unsecured funding.  Deposits can stem from retail or corporate counterparties, from central banks, financial institutions or others. They constitute a specific type of asset and liability without a contractual maturity.  Derivatives may generate very material flows, both in cash and assets. They may produce some contractual flows ‐ which may depend on the evolution of interest rates or of share prices – as well as changes in the collateral requirement due to adverse market movements. Rating downgrades may also lead to flows that may become difficult to manage for the bank. It is quite challenging to forecast flows resulting from derivatives because they can be very volatile and they depend on exogenous variables, but also on the behaviour of external counterparts.  A withdrawal of a committed liquidity line may also create huge issues for the bank, and conversely, they can provide them very good support in case of a crisis. We have already mentioned the major role of lines granted to securitisation vehicles during the crisis.

2.2. Behavioural models and specific examples on some liquidity drivers

2.2.1. General introduction to behavioural models Behavioural models are necessary to project non contractual and contingent cash flows, and the exercise of liquidity options under the various scenarios considered. They are denominated “behavioural models” as they serve the purpose of modelling the behaviour of the counterparties. Behavioural models are usually classified in three categories:  Structural models take a micro‐economic approach. They focus on the principle that economic agents try to maximise their utility. Therefore, they rely on the arbitrage function of the customer. The issue with those models is that under the same circumstances, all clients should have the same behaviour. For example, there would be a kind of cliff effect as soon as interest rates would reach a certain level. This is not the case in practise, clients have

different behaviours, because they have different risk sensitivities, different levels of information of different purposes when managing their assets.  On the opposite, statistical models are based on behavioural databases and rely on a much more pragmatic approach. The model is derived directly from the observation of how amounts evolve depending on the evolution of some exogenous data. They focus on a macroeconomic approach. There is a risk of getting results that may be counterintuitive and that may not correspond to the expected behaviour of clients and counterparts.  Mixed models, as the name implies, try to combine both approaches. The average behaviour of clients corresponds to the strategy where they try to exercise their options as optimally as possible, but the behaviours are not uniform and need to be analysed on large populations. For example, the model will forecast renegotiations on residential mortgages in case interest rates increase, through reasoning on segments of the population. As a rule, behavioural models should be built on large populations and can forecast mostly an average behaviour. It is practically not possible to do this on a line by line basis. Some important principles need to be taken into account when developing behavioural statistical models:  Databases constitution. Developing behavioural models requires sufficient data. The database should be long enough to model the middle / long term trends; the depth of the historical database needs to be commensurate with the duration of the cycles. Client by client information is costly: there is a need to aggregate information in categories (scoring, year of origination…). It may also be necessary to focus on the most material types of assets. Data on the various on balance sheet and off balance sheet items should be complemented with historical market data.  Behavioural modelling is event driven. The purpose is to analyse mathematically the causes of the events in order to be able to simulate them. Events taken into consideration may be new contract production, the setting of contract price (e.g. client remuneration rates), the setting of contract costs, the decision of an agent to end a contract, etc. Expert advice can be integrated in the modelling, in case there is no sufficient data to properly develop the model or there are doubts that past observations would really reveal the future. More in general, any pure statistical output defined for both liquidity and interest rate risk, should be “enriched” via the analysis of the following additional factors:  The bank should take into account the actual phase of the business cycle (level and steepness of the Interest Rate curve), especially as regards its impact on client behaviour (factor more related to interest rate mapping, based also on expert evaluation)  The behaviour of clients may change a lot depending if the economy is in a normal situation or in a crisis situation. Under stress scenarios, behavioural models should be significantly adjusted. As for most of similar models:  The bank should incorporate in its forecasts a cushion for model risk. In some cases, it is designated as a reserve for unexpected flows.  The model should be tested on samples independent from those used for model development, and for a different period of time (“out of sample” or “out of time” validation).

 The quantitative experts in charge of model development should also test the fitness of the model using the usual statistical toolkit, they should for example test the significance of parameters, check possible collinearity between variables, They should also provide for an appropriate back‐testing, by comparing the forecasts derived from the model with the observed evolution of the aggregates, as well as check that there is no major difference between the development versus the validation sample. They should also be aware of the “extrapolation risk”: a model may be valid under normal circumstances, but not any more in case of stress. In general, the following classes of balance‐sheet items may be subject to modelling:  Sight items (i.e. sight deposits, saving deposits, overdrafts, revolving credit lines). They are subject to moves that are more or less linked with arbitrages on interest rates. Additionally, the possible arbitrage from sight deposits to term deposits and conversely should be taken into account.  Items with a prepayment option. It is the case for example with housing loans. In case interest rates decrease, clients will tend to prepay their loans.  Undrawn credit facilities and guarantees: models can try to forecast the conditions under which they may be drawn.

2.2.2. The specific issue of assets and liabilities without a maturity, NoMALs, and some examples of approaches used to model their maturity The acronym NoMAL means non‐maturing assets and liabilities, and these correspond to the items in the balance‐sheet with no contractual maturity. The most typical examples of those are savings and sight deposits, credit card loans or variable mortgages on the asset side. They present a major issue for liquidity modelling, as it is difficult for banks to model cash‐flows, that are essentially non contractual. Different approaches have been developed to simulate their behaviour. The most simple approach is to make a direct assumption on the maturity of the asset, or to distinguish between a stable (or sticky part) that we have a longer maturity and a less sticky part with a shorter maturity (see 2.2.3.1.2.). There exist nevertheless more sophisticated methodologies and we will describe some of them hereafter. Some of them are used more for the management of interest rate risk in the banking book or assets/Liabilities management than for managing liquidity risk. The Bardenhewer and the Jarrow‐Deventer models are in the first category, the first one being mainly used to develop replicating portfolios for the management of interest rate risk, the second one to price the optionality linked with some instruments. Nevertheless, the first step of the Bardenhewer model can also be used to forecast the evolution of the deposit amount.

2.2.2.1. Replicating portfolio models (e. g. Bardenhewer7). Those models aim at replicating NoMALs into a portfolio of simple instruments, such as bonds or commercial papers, presenting similar cash‐flows. They use a three stage approach:  One needs to project the stock of NoMAL account balance. This may be done by adding some trend to the current amount, the form of which may be determined by estimation or by

7 Bardenhewer, M. (2007), “Modeling Non‐maturing Products”, In Matz, L. and Neu, P. (eds.), Liquidity Risk Measurement and Management, Wiley, 220‐256

expert knowledge. Kalkbrenner and Willing (2004) assume that the evolution of the NoMAL amount is governed by normal increments. Neu (2007), Vento and La Ganga (2009) model the future NoMAL account balance with a slightly more sophisticated approach. The NoMAL amount at time t+1 is explained by the existing NoMAL account balance, time and a normally distributed error term. A linear trend for example would look as follows:

∆ , ̅

The terms in , ̅ introduce a dependence to market rates, I representing the different

maturities, , being the market interest rate for maturity I at time t and ̅ is the average interest rate for maturity on the horizon of the observation. is the interest rate applied to the customer at time t and its average on the full time horizon. ∆ represents the linear trend underlying the evolution of the volume.  Then NoMALs are converted into a replicating portfolio. For this purpose banks may use an optimisation procedure to determine the weights of financial instruments in a replicating portfolio such that the volatility of the difference between the return from a replicating portfolio and the customer interest rate on the NoMAL is minimised. For example, we can try to replicate the asset with zero coupons of maturities 1 month, 2 months, 3, months, 1 year, etc. Therefore, the rate of the NoMAL is a linear combination of the zero coupons:

⋯ The various weights can be calibrated on historical data: they are also used to determine the weight of the various assets in the replicating portfolio.  Volume changes can be decomposed in a deterministic component (distributed over the maturities) and an unexpected component (covered by the money market account, i.e. shortest maturity). Maturing instruments are always renewed at the same maturity. Volume changes are compensated by buying additional or selling existing tranches of specified instruments. The weights assigned to the various maturity buckets is the final output of the estimation. The inputs are the trend, historical data of interest rates and historical data on the volume of non‐maturing products. The first step of this approach may be useful for liquidity management as the bank may deduct future cash flows from the run‐off profile, the following steps would serve more for the purpose of constituting a replicating portfolio of assets that would be used for neutralising structural interest rate risk.

2.2.2.2. The option adjusted spread (e.g. Jarrow‐van Deventer8) The purpose of this approach is to value and hedge deposits in an assets‐liabilities management strategy. This enables the realisation of sensitivity or stress tests analysis. It relies on the assumption that liquidity option embedded in each NoMAL can be priced with arbitrage‐free procedures. This price can be added or substracted as a spread to the coupon of the non‐maturing product. The final spread is denominated as the “option adjusted spread” (OAS). The key components of the OAS model are volume growth, rates paid to customers and the interest rate term structure.

8 Jarrow, R. and van Deventer, D. (1998), “The arbitrage‐free valuation and hedging of demand deposits and credit card loans”, Journal of Banking & Finance, 22, 249‐272

More in detail, Jarrow and van Deventer provide an arbitrage free procedure in order to compute present values in a stochastic interest rate environment. NoMALs are considered to be equivalent to exotic interest rate swaps, where the principal depends on the past history of market rates. Rates served differ from market rates due to imperfect competition. In literature, the difference is explained possibly by market frictions (search/switching costs), institutional realities (regulatory barriers) or adverse selection problems under asymmetric information. Jarrow and van Deventer use a “market segmentation” argument: banks alone and not individual investors can issue demand deposits and credit card loans: they have more leeway to apply customer rates that would differ from market rates. Indeed, there are significant regulatory restrictions and entry or mobility barriers associated with the demand deposit and credit card loan markets. Due to the fixed cost of purchasing computer equipment and technology, data feeds, as well as capital requirements and the necessary accumulation of expertise, only a limited number of banks can issue demand deposits. It results from this that the interest rate on demand deposits is lower than the interest rate on treasury markets. Sight deposits in financial institutions are considered to be comparable to exotic interest rate swaps, where the principal depends on the history of market rates. This provides sufficient elements to price and hedge those financial instruments. Using the risk neutral valuation procedure, the value of the demand deposits at t=0 represents the initial deposits, plus any changes in the deposits over time (which correspond to inflows or outflows), less the return of the deposits in the penultimate period discounted at maturity minus the present value of the aggregate cost to the deposits.

1 1 0 0 1 1 Where D(t) is the volume of demand deposits at time t, B(t) is the value of the zero‐coupon bond of maturity t, and i(t) is the interest rate served by the bank on demand deposits. This is equivalent to:

∑ 0 1 which shows that the net present value of demand deposits can be positive. The present value of the demand deposit liability to the bank at time 0 is:

0 0 0 This equals to the initial demand deposits less their net present value. Therefore, the key elements for the computation for the option adjusted spread are the expected amount of deposits, rates paid to customers and the term structure of interest rates. The Jarrow‐van Deventer paper uses the Heath‐Jarrow and Morton model to compute forward rates. There is a constant spread between market rates and demand deposit rates and the amount of deposits depends linearly of the market rate.

2.2.2.3. Using a parametric survival model (Musakwa9) Utilising a parametric ‘survival’ models can help to handle timing of stochastic cash‐flows. Under this approach, the maturity of deposits is model similarly to life expectancy (a “survival” model) and the various NoMAL accounts are considered independently. They are all characterised by a survival function which is determined by the observed evolution of the account balance for a given business

9 Measuring Bank Funding Liquidity Risk, Fidelis T Musakwa, April 2013

30 class. This account balance at time t, denoted is equal to the sum of account balances for individuals (,, i.e. ∑ ,. Nevertheless, as we are interested in cash‐flows corresponding to decrements, we shall transform the individual volume function into a decreasing one with the following transformation:

, min, It is assumed that there will be no future production. The proportion of NoMALs whose time on balance will exceed t is denoted . In discrete time, it is inferred from , by comparing the value of this function for the beginning and the end of the time period (decreases in the global volume of NoMALs is explained by subjects exiting the bank’s book, that are treated as “deaths” in a survival function approach). There are key differences between modelling cash‐flows and lives:  Cash flow modelling is scenario dependant. The evolution of the amount of deposits depends on some exogenous variables like the level of interest rates or some macroeconomic variables. It may be much more difficult to identify and model such drivers for life expectancy. Examples of bank‐specific factors to be taken into account would include: credit rating downgrades, significant operational losses or credit risk events and/or negative market rumours about the firm. Market‐specific factors include disorder in capital markets, economic recession, and payment system disruption.  The time origin to be used as a basis for “survival” analysis of financial products is unclear. It is necessary to determine the time origin for the different run‐off profiles. Musakwa suggests to take the moment where the amount was maximum for each deposit, moving backwards. Some drawbacks of the approach can be highlighted:  It ignores potential correlations between ‘survival’ times of different assets and liabilities. It could significantly be improved on this.  The evolution of deposits is not binary, they can be withdrawn progressively. When aggregating a sufficient member of deposits, this can nevertheless become a good proxy.

2.2.3. Some more specific examples of NoMALs

2.2.3.1. Sight deposits

2.2.3.1.1. Definition and general considerations The main characteristics of deposits are the following:  The client rate is close to zero, which means that the bank can get a positive margin most of the times on those liabilities, except when market rates are negative.  Their amount is usually very stable and it grows slowly, providing a smooth margin.  The client disposes of many options, one extreme being simply withdrawing the deposit, the other one letting the deposit dormant (when there is a very low probability of an inflow). We can highlight the following specificities in the modelling:  The bank should constitute a database with as much information as possible on its deposit base and on client’s behaviour. This should include in particular their amount, the corresponding remuneration, and information on the client’s activity and on cases where the

deposit account was closed.  All those variables need to be modelled: as a basis, the bank should be able to forecast the remuneration in comparison with other products and competition, and based on this and on some exogenous variables, the probability that the client may close its account or that the account may become dormant. If not the case, the bank should model the evolution of the corresponding amount. The evolution of the balance is a function of multiple factors: o Funds may be more or less liquid, depending on the term and conditions set by the bank around the withdrawal of funds. o Investors will leave their funds in safer banks if they have some assurance that they will be protected in case of turmoil. This depends on the reputation of the institution – a good credit rating can help– but also on possible legal or contractual guaranties on deposits. o In principle, interest rates have a positive impact on deposit amounts, but there is a limit in the possible amount to be collected. o The macroeconomic environment plays also a major role, as it defines both the demand for deposits and the overall competitiveness of the market. The model should incorporate material structural changes in the environment, in particular changes in the regulatory framework, competitive market environment or bank’s commercial strategies. • Deposits should be clustered into uniform segments, corresponding to the assets classes that we described under the Fiedler approach. Those segments should present significant differences in their behaviour with the average deposit: the bank should rely on techniques such as analysis of variance. In particular, a distinction should be drawn between sight and saving deposits. One may also distinguish between different types of depositors. Basel III relies in particular on the distinction between retail, non‐financial corporate and financial depositors, among others. A more granular segmentation could also be used, based on the characteristics of customers (their revenues, their age, etc), the way they have created their account (on line?) the stability of their relationship with the bank or the type of offer they benefit from (promotional rates?). The cluster definition should be stable and robust. If there may be some correlation effect between clusters, it should be made explicit. A materiality threshold for clusters may be used in this regard.  For each cluster, the bank shall estimate the behaviour of deposits and their expected life under various assumptions. The approaches mentioned here above can be relied upon. Among those, the bank may in particular use a very simple time‐dependent model, where the outstanding amount is a simple function of time A(t), with possible breaks in the trajectory. This approach tends to ignore the influence of the environment on the behaviour of customers; a more sophisticated modelling will introduce other factors that may explain the evolution of the balance (the techniques described previously as regards NoMALS may be used here). Usual techniques should be used in this context, as making some of the series stationary if necessary and introducing time lags.

 We already mentioned some of the variables that may be considered as inputs in the model. Interest rates in particular have to be considered, and more specifically the extent to which they differ from the rates practices by competitors.

2.2.3.1.2. Core / sticky deposits vs. other types of deposits It is obvious that some deposits are more sticky than others, and that the run‐off rate will depend highly on their nature and the reason why they are held by clients. Stickiness can be defined as the sensitivity to normal movements in the interest rate. Matz identifies 4 reasons for a client to hold deposits: safety (which is increased if there is deposit insurance), convenience (deposits at local branch), liquidity and interest rate. These reasons drive the stickiness of corresponding deposits. Banks and regulators usually designate the stickiest part of the deposits as being the core deposits. Nevertheless, it is not so easy to define this notion. Some elements shall at least be considered:  The deposit’s insurance status is the most important characteristic in determining the sensitivity of deposits to risk or stress. According to case studies provided by BIS, uninsured deposit are a major source of liquidity risk.  Bank/depositor relationship also has a significant impact on the stability of a deposit. Core volume should be defined with a proper level of conservatism. Core deposits will be considered as more stable in the long term (>1 year); non‐core deposits may decrease rapidly in the short term. The non‐core portion shall be allocated only to short term time buckets when computing the forward looking exposure.

2.2.3.2. Assets with prepayment option The option of an early repayment is one of the most common liquidity options, it may be exercised with payment of a penalty, which represents a transaction cost. We can identify two main categories of repayment: • Behavioural prepayment are not directly related to the evolution of market rates. They are purely idiosyncratic and concern a single borrower. In general, they are linked with sociological explanations, such as geographic mobility, deaths, disability, change of the financial situation of the customer, or of his civil situation. They correspond to the minimal part of prepayments than cannot be avoided. They can also be designated as structural prepayments. • Financial prepayments are more closely related to trends in market rates. They result from arbitrages done by clients. As regards the modelling, the principles already mentioned still apply. The specific explanatory variables to be taken into consideration are the following: • As regards the behavioural component: gender, employment/salary, age, geographic positioning, length of the loan, loan to value, etc. • As regards the financial component: financial incentives resulting from the analysis of market related parameters should be analysed, in particular, the difference between product rate and market rate at the time of the prepayment. Nevertheless, not all mortgages will suddenly prepay and not all debtors are so skilled to value the convenience to exercise the option. The 3 most important variables to be taken into account are interest rate spread, seniority/residual maturity and burnout. Burnout is the tendency for prepayments to drop

after rates fall, rise, and fall again. In other words, when interest rates keep on dropping, those who can benefit by taking advantages of refinancing will have done so earlier when rates declined in previous periods. It should be noted that there is always a lag between the moment where interest rate decreases and the observation of the prepayment phenomenon. In simulation, default and prepayment have similar patterns. The prepayment option can be considered as being similar to a default with a 100% recovery rate. It is therefore possible to score prepayment similarly to default.

2.2.3.3. New production modelling One needs to simulate transactions linked with increasing the business with clients as this is also a common type of liquidity option. 3 types of hypotheses are usually used: either the outstanding may be constant, increase according to some budgetary assumptions (e.g. 5% per year). It may also be considered that the new production will remain constant. For a more sophisticated modelling, some additional factors may be taken into consideration. The bank may try to develop its business, may have launched promotional campaigns for this purpose, or apply perequation in the tarification to attract certain types of new clients. Some exogenous factors may influence the modelling as well, as the global evolution of households debt, sociological factors, seasonality, and global customer developments.

3. The supervisory approach of liquidity and its latest update, Basel III

3.1. A history of the supervisory approach regards liquidity Supervisors have taken different steps over time for tackling the issue of liquidity risk. The Basel Committee of Banking Supervisors (BCBS) has published a series of papers that signal its increasing awareness of the impact and of the complexity of liquidity risk and through which it has updated regularly its prescriptions on liquidity risk management:  In 1992, the committee issued A framework for measuring and managing liquidity risk: supervisory authorities have to differentiate between large international and domestic banks when monitoring liquidity risk; different methodologies to measure liquidity risk are suggested, based on the maturity ladder or on scenario analysis.  In 2000, the BCBS illustrated recent evolutions in liquidity management and defined 14 key principles for managing liquidity risk. They stressed on the importance to design different solutions for both day to day management and emergency situations, as well as the relevance of monitoring and measuring the net funding requirements. The paper did not specifically identify dominant methodologies to assess and manage liquidity risk. The link between liquidity risk and other types of risks was also evidenced.  In 2006, a new paper considered the impact of off‐balance sheet instruments and of on‐ balance sheet contracts with embedded optionality. It made a specific differentiation between funding liquidity risk and market liquidity risk. Managerial practices of banks were still diverging a lot at that time.  In February 2008, the committee issued Liquidity risk: management and supervisory

challenges. As the financial crisis had already begun, the committee explored some new challenges of liquidity risk management. It highlighted in particular the impact on liquidity risk of recent financial innovations and capital markets developments: for example, the fact that banks relied more on capital markets funding, the relief that securitisation had provided to help banks manage their liquidity risk, and the additional needs it creates during periods of crisis, the complexification of financial instruments which complicates also liquidity risk monitoring, the increased use of collateral for funding, etc.  In June 2008 with its Principles for sound liquidity risk management and supervision, the committee offered guidance on the risk management of funding liquidity risk. In particular, it highlighted the importance of allocating liquidity costs, benefits and risks to all significant business activities. They underlined the necessity to measure the full range of liquidity risk, including contingent liquidity risk and the need for designing severe stress test scenarios. The objectives of the current supervisory framework of liquidity can be summarised with a few priorities: supervisors aim at ensuring survival to a fixed horizon in the event of a severe funding crisis, they want to limit excessive risk taking and to promote adherence to best practices, they try to minimize systemic risk and also to take countermeasures against possible market failures.

3.2. New ratios: LCR and NSFR As the result of the increasing awareness of regulators, they have decided to prescribe the calculation of 2 new regulatory metrics that aim at capturing in a standardised manner the 2 main aspects of liquidity: the ability of the bank to fund itself efficiently in the short term, and the stability of its funding on a longer time horizon. This led to the definition of the Liquidity coverage ratio (LCR) and of the Net stable funding ratio (NSFR).

3.2.1. Description of both metrics Both metrics belong to the group of hybrid indicators that we mentioned earlier. They rely on the measurement of some of the main aggregates of the balance sheet that are relevant for liquidity risk, with the introduction of a dynamic element, as some hypotheses are applied on those aggregates to account for the fact that they may evaluate considerably in the short or long term.

3.2.1.1. LCR The purpose of LCR is to calibrate a buffer of high quality liquid assets (HQLA) to cover liquidity risk in a one month horizon, liquidity risk being measured by net outflows. LCR is calculated with the following formula: Total net cash outflows over the next 30 calendar days The calibration is done under a stress scenario that is uniformly calibrated for all banks. This scenario entails a combined idiosyncratic and market‐wide shock that would result in:  the run‐off of a proportion of retail deposits  a partial loss of unsecured wholesale funding capacity  a partial loss of secured, short‐term financing with certain collateral and counterparties  additional contractual outflows that would arise from a downgrade in the bank’s public credit rating by up to and including three notches, including collateral posting requirements

 increases in market volatilities that would impact the quality of collateral or potential future exposure of derivative positions and thus require larger collateral haircuts or additional collateral, or lead to other liquidity needs  unscheduled draws on committed but unused credit and liquidity facilities that the bank has provided to its clients  the potential need for the bank to buy back debt or honour non‐contractual obligations in the interest of mitigating reputational risk. The stress scenario specified incorporates many of the shocks experienced during the crisis that started in 2007 into one significant stress scenario for which a bank would need sufficient liquidity on hand to survive for up to 30 calendar days. Regulators have also defined the fundamental characteristics of the buffer of high quality liquid assets: they present a low risk, they are easy to value, they present a low correlation with risky assets, they are listed on a developed and recognised exchange. The market on which they are traded is active and is quite sizable. The assets have a rather low volatility, and benefit of flight to quality in case of a crisis. This time horizon was chosen as the relevant period because it was viewed as long enough for central banks and governments to take the necessary emergency measures to calm a widespread market crisis of liquidity. Some operational requirements apply also to the bank, which should monetise regularly a representative portion of the assets and take into account only unencumbered assets. The corresponding stock should be under the control of the function in charge of managing the liquidity of the bank.

3.2.1.2. NSFR NSFR focusses on a longer time horizon and has been developed with the purpose of promoting resilience over the long term. It requires banks to have stable enough sources to fund their on‐ and off‐balance sheet assets, so that they would be able to survive in case funding sources would drain. Therefore, banks should not rely too much on short term funding. It directly limits maturity transformation by banks. This indicator is calculated as the ratio between the amount of available stable sources of funds and the level of stable assets, adjusted for their ability to be liquidated, over a one year horizon. Stable sources of funds are identified based on their relative stability. It depends of their contractual maturity and on the propensity of funding providers to withdraw their funding. Liabilities are split into 5 categories, each of which being associated with a multiplicator. They are summarised in the table here under:

Factor Instrument  Total regulatory capital 100%  Other capital instruments and liabilities with effective residual maturity of one year or more

 Stable non‐maturity (demand) deposits and term deposits with residual 95% maturity of less than one year provided by retail and SME customers

 Less stable non‐maturity deposits and term deposits with residual 90% maturity of less than one year provided by retail and SME customers

 Funding with residual maturity of less than one year provided by non‐ financial corporate customers  Operational deposits  Funding with residual maturity of less than one year from sovereigns, 50% public sector entities (PSEs), and multilateral and national development banks  Other funding with residual maturity of not less than six months and less than one year not included in the above categories, including funding provided by central banks and financial institutions

 All other liabilities and equity not included in above categories, including liabilities without a stated maturity 0%  Derivatives payable net of derivatives receivable if payables are greater than receivables

The definition of stable deposits is consistent with the one used for LCR. Some behavioural assumptions have been specified by regulators: for example as regards funding with options exercisable at the bank’s discretion, banks should as a rule assume that they will be exercised at the earliest possible date. A similar approach is applied to compute the required amount of funding. The factors applied to the respective categories are supposed to replicate the amount of the asset that will need to be funded, either because of a roll‐over or because it could not be sold or used as collateral in a secured borrowing transaction in the next year without a significant cost. Those various categories are also summarised in the following table:

Factor Components  Coins and banknotes  All central bank reserves 0%  Unencumbered loans to banks subject to prudential supervision with residual maturities of less than six months

5%  Unencumbered Level 1 assets, excluding coins, banknotes and central bank reserves

15%  Unencumbered Level 2A assets

 Unencumbered Level 2B assets 50%  HQLA encumbered for a period of six months or more and less than one year  Loans to banks subject to prudential supervision with residual maturities six months

or more and less than one year  Deposits held at other financial institutions for operational purposes  All other assets not included in the above categories with residual maturity of less than one year, including loans to non‐bank financial institutions, loans to non‐ financial corporate clients, loans to retail and small business customers, and loans to sovereigns, central banks and PSEs

 Unencumbered residential mortgages with a residual maturity of one year or more and with a risk weight of less than or equal to 35% 65%  Other unencumbered loans not included in the above categories, excluding loans to financial institutions, with a residual maturity of one year or more and with a risk weight of less than or equal to 35% under the Standardised Approach

 Other unencumbered performing loans with risk weights greater than 35% under the Standardised Approach and residual maturities of one year or more, excluding loans to financial institutions 85%  Unencumbered securities that are not in default and do not qualify as HQLA including exchange‐traded equities  Physical traded commodities, including gold

 All assets that are encumbered for a period of one year or more  Derivatives receivable net of derivatives payable if receivables are greater than payables

100%  All other assets not included in the above categories, including non‐performing loans, loans to financial institutions with a residual maturity of one year or more, non‐exchange‐traded equities, fixed assets, pension assets, intangibles, deferred tax assets, retained interest, insurance assets, subsidiary interests, and defaulted securities

3.2.2. Some thoughts around LCR and NSFR

3.2.2.1. The debates around the choice of the supervisory reference metrics Opposition to the LCR concept centres around three concerns:  As any kind of standardised metric, LCR promotes a global and uniform approach which does not sufficiently consider local differences. Whatever the type of metric, regulators always have to deal with the trade‐off between relying on indicators that are tailored to the specific risk profiles of the banks ‐ at the expanse of not being able to check the appropriateness of the assumptions taken and of being unable to get a global picture of the position of banks ‐ and developing an uniform approach ‐ that may be inaccurate for some profiles. The solution to this dilemma has always been to complement the computation of harmonised metrics with a requirement for bank to be aware of their specificities and to develop tools to measure and monitor the corresponding risks.  A simplified formula, even one with as many elements as the LCR, would not be able to approximate a true stress test closely enough to be useful without providing distorted

incentives. The underlying scenario is a composite of the ones usually used by banks; it is not specific enough to concretely represent configurations that banks may have to face. Therefore, it cannot be considered as the sole indicator for banks to steer their activity as regards liquidity risk.  There would be risks that in a crisis all non‐liquid assets according to the regulation would de facto become non liquid; the narrow definition of HQLA may increase concentration risk towards sovereign exposures. It is also quite often highlighted that the implementation of LCR has highly increased the demand for assets that are classified in the HQLA category, which may create a challenge for banks. The first and the second argument plead for the need for banks to invest significant resources in developing their own liquidity management framework, that needs to be consistent and articulated with the regulatory requirements, but should not be limited to them. The 3rd one is more difficult to address, unless by trying in the next years to observe market developments and eventually adjust regulatory definitions so as to make them more appropriate. As a complement, we tried to analyse LCR with the criteria developed by Matz that were described previously:

Comprehensive: incorporates all assets, liabilities and off‐ Yes balance sheet sources and uses of liquidity

Flexible: can show assets (loans as well as investments) as Yes both sources and uses of liquidity. Can show liabilities as stable or volatile

Uses prospective, not historical cash flow data Yes

Reflects the fact that liquidity sources and uses are Only one scenario, because the purpose is to have a scenario specific comparable metric for all banks. Combination of the worst scenarios to be considered in stress tests

Reflects the temporal nature of liquidity risk Reflects only a one month time horizon

As regards NSFR, we can also highlight some of the most common critics that have been formulated:  If the NSFR is viewed as a one‐year stress test, its designers faced the difficult task of evaluating reactions over a one‐year period of liquidity crisis. A 30‐day crisis scenario is much easier to construct, because many of the potential reactions, such as raising equity, changing business models, or selling units, are difficult to take in that time interval, especially under adverse conditions. Within one year, banks have much more room to react and authorities a more leeway to alter the environment.  The NSFR was not really designed as a stress test. In practice, it appears to represent a set of norms for dealing with funding mismatches that seemed broadly reasonable to the staff and members of the Basel Committee, but without an underlying quantitative basis.  The calibration of the ratio was a very sensitive issue, as there was a risk to limit too drastically maturity transformation which is one of the main functions of banks in the financial system. NSFR would create an excessive constraint for some types of business models which need to rely on short term funding (this is the case for some specialised lenders). The current calibration tries to strike this very delicate balance. Time will show if some adjustments are necessary.

An overall criticism about the regulatory framework as it results from the various BCBS papers relies on the fact that it may be difficult for banks to comply with a very comprehensive and quite complex set of requirements with possible dependencies and interferences. In other words while trying to comply if one of the regulatory requirements, the bank may take remedial actions that will negatively impact compliance with one of the other requirements. Some of the banks’ deleveraging strategies to comply with the regulatory requirements are presented in the following table:

Risk‐based capital ratio Leverage ratio LCR NSFR

Sell assets Cut repos Sell level 2 assets Sell level 2 assets Cut interbank loans or reverse Cut derivative positions Cut interbank loans or Sell non‐HQLA or non core repos reverse repos assets Cut commitments Do not roll over maturing loans Reduce maturity of other loans For example, the bank may increase its amount of repos to comply with LCR, which may have a negative impact on the leverage ratio. It may sell HQLA assets to increase its solvency ratio, with a negative impact on LCR. Collectively, if banks implement deleveraging actions at the same time, they may also create feedback loops. The use of harmonised metrics may lead banks to synchronise their actions more than in a less regulated environment.

3.3. New monitoring and reporting requirements After the financial crisis, regulators have also decided to increase the supervisory liquidity reporting requirements. Those requirements are listed in the CRR.  This concerns firstly LCR and NSFR and inflows and outflows corresponding to LCR that shall be reported on a monthly basis.  Bank shall also report the liquid assets they hold. Among those, cash and exposures to central banks, other transferable asset that are of extremely high or high liquidity and credit quality, transferable assets representing claims or guaranteed by a set of guarantors identified in the regulation10, etc. The reporting shall focus on unencumbered liquid assets and stand available within collateral pools to be used for the obtaining of additional funding  Banks are also supposed to report additional liquidity monitoring metrics to allow competent authorities to get a comprehensive view of the liquidity risk profile. Those metrics have been defined by the EBA in the form of an implementing technical standard. They include concentration of funding by counterparty, concentration of funding by product type, prices for various lengths of funding and roll‐over of funding. The initial proposal of the EBA included a maturity ladder (without behavioural assumptions) and some details on the liquid assets buffer. This part of the technical standards has been retained by the European commission, due to its partial redundancy/ partial inconsistency with the reporting on liquid assets in the context of LCR.

10 Central government of a member state, central banks and non‐central government public sector entities in the domestic currency of the central bank, BIS, IMF, EFSF, etc.

Pending the entry into force of reporting requirements concerning the maturity ladder in particular, the ECB has put in place some additional reporting requirements for banks under its direct supervision. Under the denomination of the short term exercise (STE), they include in particular a tailor‐made maturity ladder. This maturity ladder is intended at enabling a liquidity gap analysis. It is based on contractual cash flows. Some more details on this will be provided later.

4. Going further: calibrating supervisory measures, notably in the form of a liquidity buffer

4.1. The necessity to define additional supervisory measures and the use of stress tests in this context As already mentioned, the pillar 1 metrics like LCR and NSFR are not sufficient to fully capture risks related with liquidity, because they are standardised and may not by adapted to the specific risks of the bank. They also cover only part of the liquidity risks of banks in general. For regulators, supervising liquidity risk necessitates ‐ first to ensure that the bank has a sufficient counterbalancing capacity to cover liquidity risks and – second, that its liquidity management framework is adequate. On the first aspect, the “liquidity P2 requirements” will be expressed more in quantitative terms, on the second aspect, more in qualitative terms.  Qualitative requirements: supervisors may impose on banks some specific requirements regarding liquidity management. They may for example develop additional reporting requirements, ask them to enrich their stress test framework, prescribe them to implement additional metrics to be monitored, impose some diversification on the portfolio of liquid assets, etc.  Quantitative requirements. Supervisors need to ensure that the bank’s counterbalancing capacity will be sufficient to cover future liquidity shortages. One of the aspects of this is to ensure that banks have sufficient liquidity buffers. There are 2 areas where this applies, more specifically: o Intraday liquidity risk which concerns the very short end of the maturity ladder. Banking supervisors have defined standards, but there is no pillar 1 requirement as regards the level of the liquidity buffer. This concerns both “normal” circumstances and “stressed” circumstances. Some more details on intraday liquidity risk will be provided later. o Over a longer time horizon, supervisors and banks should acknowledge the fact that liquidity is a low probability / high impact risk. Most of the metrics described up to now are very useful, but they provide only a partial view of liquidity risk. Banks need some additional tools to ensure that their liquidity buffers will be sufficient to face the variety of risks that they may be exposed to. The most convenient approach will consist in applying ad‐hoc stress scenarios, customised for the specific characteristics of the bank. In this context, “scenario analysis” should be designed to test extreme, but yet plausible events. They are in particular useful to simulate different time horizons, to have a view on the liquidity mismatches under the time horizon and to test ad‐hoc and maybe more adequate assumptions.

Of course, stress tests will not only be useful to calibrate the level of the liquidity buffers. The insight gained from stress scenarios should be decisive for developing the liquidity risk management approach, including the institution’s liquidity risk tolerance, funding strategy and contingency funding plans. Various purposes are more particularly targeted with stress tests:  Test the capacity to withstand a bank‐run (short-term counter-balancing capacity);  Assess the extent and capacity to deal with maturity mismatch. In this context, stress tests can be seen as a tool to support risk management, to determine the size of the portfolio of liquid assets.  When combined with solvency stress tests, they are used to assess potential threats to liquidity arising from solvency risks. Based on those arguments, regulators have asked banks to develop a comprehensive set of stress scenarios and to incorporate them in their liquidity risk management framework; they also rely on the use of stress scenarios they have developed themselves. In this regard, they can take 2 approaches to ensure consistency between banks:  Top‐down stress tests: regulators define a common set of scenarios and apply them on the raw data they get from the bank, taken from the supervisory reporting. This ensures consistency and comparability between banks and can be useful to set some standards. This exercise may also be helpful to challenge the bank’s internal metrics. Regulators also have the ability to simulate more situations. This approach nevertheless relies on the assumption that the balance sheet of the bank and the items that determine its liquidity will react similarly to shocks; this is not assured.  Bottom‐up stress tests: banks provide themselves the outcome of the simulations. The scenarios may be provided by regulators or partially customised for each bank. The advantage of this approach is that the models used are adjusted to each bank’s specificities, this makes theoretically results more reliable, but it is detrimental to comparability. In this approach, regulators can also hardly check the quality of the projections. The IMF has investigated approaches taken by various central banks and regulators to organise down stress tests. Here are a few highlights on their methodological choices:

 Some models consist in applying shocks corresponding to various scenarios to banks’ balance sheets. Those shocks are translated into haircuts applied on assets and run‐off rates applied to liabilities. This approach was represented by Bank of Japan, Sveriges Riksbank, Bank of Italy and Central bank of Brazil when the study was issued.

 Some models go a bit further and include some modelling of cash flows. This was the case for the Austrian central bank (OeNB) and Bank of Canada was in the course of developing such an approach when the IMF study was published.

 Those models include usually shocks to credit, market risk and interest rate risk that may be generated by stochastic simulations on market prices and macroeconomic variables (OenB and Bank of England). Bank of England developed for example the RAMSI model which includes a Bayesian auto‐regression model to simulate macroeconomic scenarios, a satellite models for credit, market risk and IRRBB and an asset price function to simulate fire sale of assets. The banks funding cost is determined based on a bank’s credit rating.

 Ultimately, those scenarios may trigger bank defaults, leading to second round and interbank contagion effects (Bank of Canada, Bank of England, OeNB). The Dutch central bank (DNB) developed for example a model with Monte Carlo simulations that permit to compute

liquidity ratios after the first and second round effects of a scenario. Some versions of the methodology also include a central bank reaction function, through which the effects of unconventional monetary policy measures on bank’s liquidity positions can be simulated. As they have been implemented by Central banks who have a specific responsibility as regards the stability of the financial system, those stress tests are produced more in a macro‐prudential perspective, namely to get a view on the whole system. The specific stress tests that banks are requested to put in place correspond more to a micro‐perspective. In the following chapters, we are going to make some proposals on how to implement top‐down stress tests.

4.2. Our methodology for stress testing a bank’s position on the mid and long term

4.2.1. Some basic steps when stress testing and some methodological requirements The approach we are going to take here will consist in the implementation of a cash‐flow analysis under different scenarios. This relies on 2 elements:  The projections will be based on a representation of the balance sheet already including some projections of cash flows on a given time horizon based on the approach defined by Fiedler. In other terms, we need to group items by asset units and to focus on the main liquidity drivers that may have an impact on their evolution.  Identifying the main liquidity drivers is a major task in itself. The list of main risk drivers may vary a lot depending on the bank’s business model: for example, margin calls will be essential for an investment bank or retail deposits for a retail bank. The bank shall then apply a given outflow rate to the various liquidity units, based on the scenarios mentioned previously.  Our methodology will consist in using the information available on the contractual outflows estimated by the bank. Stress scenarios complement this, taking into consideration shocks that would represent the behavioural aspects of the scenarios. This is naturally possible only if some information on contractual flows is available.  We shall define our scenarios. Those can be based on historical observations (past crises), but the bank should also proceed to some hypothetical stress testing. With reverse stress testing, banks will proceed to some reverse type assessment of the limit of each bank (“stress until it breaks”). Stress scenarios should incorporate realistic, but also unrealistic assumptions. There is a continuum in the severity of scenarios usually put in place by banks and regulators: ordinary course of business, mild seasonal, pronounced seasonal, mild cyclical, severe recession, mild name crisis, severe name crisis, mild systemic, severe systemic. Neither a single theory, nor a single set of ratios can capture the diverse types of liquidity requirements. In the end, it is usually recommended to define 3 types of scenarios:

o Operational and seasonal liquidity needs. They identify the needs in the ordinary course of business, i.e. the “going concern” need for liquidity. In these scenarios, banks also have to meet unexpected surges in loan demand or deposit withdrawals, as well as some seasonal needs, or to be able to take advantage of new business opportunities.

o Bank name or bank specific crises. Those correspond to the “classical” funding crisis that materialises when fund providers lose confidence in an individual bank or banking group. The most common trigger for such a crisis is credit risk and, for example, a multi‐notch downgrade. But there may be other types of triggers: for example some fraud or an

operational incident that will create doubts and erode confidence in the bank. In some studies, this shock is also designated as being idiosyncratic.

o Systemic and cyclical crises which coincide with market‐wide scenarios. They may be caused by macroeconomic corrections, capital market disruptions (banks are unable to sell investment assets without incurring unacceptably large losses) or payment systems disruptions. The great liquidity squeeze of 1966, the UK fringe banking crisis of 1974 or the subprime crisis are examples of those. No clear line separates bank‐specific and systemic crises. Sometimes, a bank‐specific crisis develops because of problems related to a systemic crisis. Or a systemic crisis can be triggered by a spreading loss of confidence caused by a bank‐specific crisis (spill‐over or contagion risk). Stress scenarios should include short, intermediate and long term events. According to the CEBS guidelines on liquidity buffers and survival periods, a survival period of at least one month should be used to determine the overall size of the liquidity buffer under the chosen stress scenarios. Within this period, a shorter time horizon of at least one week should also be considered to reflect the need for a higher degree of confidence over the very short term. We could for example include a scenario with a short acute phase of stress followed by a longer period of less acute, but more persistent stress. Obviously, the longer the stress horizon is, the more hazardous the outcome gets. Some additional elements need to be taken into consideration when developing the stress scenarios:

 Liquidity sources depend on time available. A bond that matures today is a cash inflow, one that matures in 90 days is a marketable asset. With enough time, it is possible to sell loans which can represent a drag on liquidity in the short term. Nevertheless it is quite difficult in the context of stress testing to consider the full set of actions that the bank may take on a longer time horizon (unless there are detailed and reliable elements on the liquidity management strategy of the bank on the longer time horizon). Stress tests will often rely on the assumption of a very simple liquidity management strategy being implemented by the bank.

 Most liquidity needs are not instantaneous shocks, they develop in stages.

 Short term shocks may be different in nature from long term shocks. In a short term funding crisis there is almost no time to obtain liquidity from some sources. In the longer term, there are more possibilities, like loan securitisations or real estate sale leasebacks. Additionally, we should take some criteria into consideration as regards the stress testing methodology itself:  Models must be kept sufficiently straightforward, transparent and flexible in use.  2 types of elements to be taken into consideration when designing stress tests: past experience and expert judgement.  There will always be considerable uncertainty surrounding the estimates associated with scenario outcomes. This is an important caveat to keep in mind.

4.2.2. Steps for stress testing

4.2.2.1. Getting the unstressed cashflow data

4.2.2.1.1. What kind of data is available? We will rely on the data provided by banks in the context of supervisory reporting, i.e. the regulatory maturity ladder, LCR and NSFR. The regulatory maturity ladder includes a detailed view of the bank’s inflows and outflows, as well as of the counterbalancing capacity. Here are some more details on the data to be reported:  Outflows: liabilities resulting from securities issued, liabilities from secured lending and capital market driven transactions, with a split based on the nature of the corresponding collateral, liabilities resulting from deposits by customers that are not financial customers, liabilities resulting from deposits by customers that are financial customers, FX swaps maturing, amount payable due to derivatives and other cash flows.  Inflows: monies due from secured lending and capital market driven transactions, FX swaps maturing, amount payable due to derivatives paper maturing in own and other cash flows  Counterbalancing capacity: cash, exposure to central banks, unencumbered Central Bank eligible collateral, other unencumbered non central bank eligible, tradeable assets und undrawn committed credit lines granted to the reporting institution Therefore, our stress tests will be cash‐flow based and rely mainly on a contractual view of cash flows as this is the approach taken in regulatory reporting. The maturity ladder includes for example information on the run‐off of term deposits, of securities issued by the bank or of its secured funding. The detailed description of the reporting requirement on the maturity ladder is presented in annex 1. There are some inconsistencies between the LCR reporting framework and the maturity ladder. Reconciliation between both approaches is currently very complicated. Nevertheless, for the purpose of stress testing, we will have to complement the maturity ladder data with some elements taken from LCR and NSFR reporting. In some cases, it is necessary to make choices between the different data sources; efforts currently done by European regulators to facilitate reconciliation between LCR and the maturity ladder will be useful in this regard.

4.2.2.1.2. Choice of the main liquidity drivers to be taken into consideration The main liquidity drivers to be taken into consideration have been mentioned. Here are those that are even more relevant in the context of stress tests and how we are going to derive them from available data:

 Deposit run‐off. Deposit run‐off is a major source of funding stress and is always the first element that is taken in consideration when stress testing liquidity risk. We will base our proxies on the LCR definitions as regards stable vs. less stable deposits for the retail side and operational deposits vs. non‐operational deposits on the corporate side. In LCR, stable retail deposits are identified based on the following criteria: those are retail deposits guaranteed by a deposit guarantee scheme, where the deposit is part of a part of an established relationship making withdrawal highly unlikely or held in a transactional account. Criteria to identify established relationships are also provided in LCR, in particular the duration of the contractual relationship, the type of relationship (clients have a more stable relationship with their bank if they have a borrowed for residential loans or other long term

loans) and the number of active products the customer holds. According to the regulation, a transactional account is an account where salaries, income or transactions are regularly credited and debited respectively against that account. Stable corporate deposits are operational deposits, namely those maintained by the depositor in order to obtain clearing, custody, cash management or other comparable services in the context of an established relationship with the credit institution; other types of established relationships may be taken into consideration. They may also be held in the context of a common task sharing within an institutional protection scheme.  Off‐balance sheet commitments. According to BIS, commitments to corporate borrowers do not appear to be a material source of stress. Liquidity support to asset backed commercial paper programmes is potentially a much greater and more acute source of stress than loan commitments. Therefore, we should try to identify clearly those commitments, drawing a distinction between the various types of counterparties (Financial vs. non‐financial corporate in particular).  Loan pipeline back‐ups. Banks may provide their support to securitisation pipelines that may turn into major sources of liquidity risk. There is indeed a risk that they will be unable to distribute the assets and that they will have to carry them on the balance sheet and to fund them accordingly. As a result, the bank may need to increase its reliance on wholesale funding markets. Under stressed conditions, there should be higher drawdown rates on those exposures.  Collateralisation of intraday credit risk and other exposures of payment and settlement banks to the stressed firm. Some clearing and settlement banks may try to increase their collateral requirements in case of a crisis, in the form of assets or deposits. Such requests may also result from clearing and settlement agreements. It can drain a bank’s buffer assets.  Secured funding: Access to secured funding is pro‐cyclical as haircuts increase, securities valuation decrease and counterparties change their credit risk limits in case of a crisis. Collateral does not shield out against an idiosyncratic shut‐out of funding, but reduces it significantly  Reliance on wholesale funding or an excessive wholesale funding concentration may also be an issue. A good access to the wholesale interbank market may prevent banks to invest in liquid assets or help them to compensate a relative insufficient retail deposit base. This may turn into a major weakness in case of a crisis. Such a crisis may result from a solvency problem of the borrower or from a market freeze due to informal frictions such as adverse selection.  Derivatives and foreign currency funding. Market evolutions and rating triggers may have an impact on the collateral provided for derivatives. It is of secondary importance for most of the banks, but may not be for those which are active on the markets.

4.2.2.1.3. Our methodological choices to derive unstressed data from supervisory reporting As the main basis of our calculations, we are going to use the list of items reported in the short term exercise maturity ladder. The detailed structure of the ladder is presented in annex 1. The list of the main item to be taken into consideration is summarised in the following table: LT unsecured issuances maturing Unsecured funding ST paper due Secured issuances maturing Secured funding Repos maturing Retail deposits outflows

Corporate deposits outflows Deposits

Outflows Central Bank deposits outflows Financial deposits outflows Other deposits outflows FX‐swaps outflows Derivatives outflows Other outflows

Reverse repos Retail inflows Corporate inflows

Central Bank inflows Other entities inflows Fin. Inst. (not within IPS) inflows

INFLOWS IPS inflows FX‐swap inflows Derivative inflows Other inflows

Cash Central Bank exposures 0% RW securities ECB eligible CAPACITY

20% RW securities Covered bonds Corporate bonds RMBS Other central bank eligible assets Non‐central bank eligible equities Other non‐central bank eligible assets

COUNTERBALANCING Undrawn committed credit lines

This segmentation reflects most of the drivers mentioned previously, but omits some important elements:  Off balance sheet commitments are probably underestimated. Committed credit lines may not cover the full range of commitments that the bank may have provided. We will extract this information from the LCR reporting.

 LCR also includes some elements on collateral posting requirements due to a downgrade or on market moves that may be omitted as well in the regulatory maturity ladder. It may also provide some useful information on the buy backs that the bank may have to do to honour non‐contractual obligations in the interest of mitigating reputational risk. It is also necessary to implement some proxies to have a detailed view of the balance sheet. In particular, it is necessary for assets without a maturity, to make some assumptions to allocate cash flows to the various time buckets. Our assumption will rely on a linear decrease of the corresponding items. Possible liquidity support from the central bank will not be considered here.

4.2.2.2. The global outline of our scenarios The full roll‐over of the positions will be the baseline scenario. We will focus on 2 additional scenarios from the list we mentioned earlier:

 An idiosyncratic shock, resulting from a short term loss of confidence in the institution. There would then be no rollover of unsecured wholesale funding whereas secured funding would be less affected. There would be significant outflows of retail funding and this can trigger demands for collateral and margin from counterparties (possible link with a credit downgrade). This scenario is on taken on a 4 weeks horizon.

 A macroeconomic stress scenario combined with a financial market stress. There would be a limited outflow of retail and corporate deposits, whereas it would be higher for other types of deposits. There would be an important decrease of unsecured funding. Secured funding would be less affected, but repo markets would highly differentiate between the types of collateral. All positions linked with markets would be impacted: derivatives would generate margin calls and higher haircuts would be applied to liquid assets. Liquidity and credit facilities to non‐financial corporations would be drawn on by counterparties. Those assumptions are summarised in the table hereunder. This scenario is taken under a 12 months horizon.

Combined Macro & Baseline Idiosyncratic Financial Time horizon 12M 4W 12M Outflows Unsecured funding (ST & LT) Roll over No roll over 50% roll over Secured funding Roll over 50% roll over 50% roll over Repos No roll‐over No roll‐over No roll‐over (maturing repo: (maturing repo: (maturing repo: increase in the CBC) increase in the CBC) increase in the CBC) Retail & corporate deposits Macro & prudential Calibrated on LCR * 2 Retail stable Roll over 6% outflow 3% outflow Retail unstable Roll over 20% outflow 10% outflow Corporate operational Roll over 10% outflow 5% outflow

Corporate non‐operational Roll over 30% outflow 15% outflow Central bank Roll over Roll over Roll over Other deposits Roll over Calibrated on LCR: Calibrated on LCR: 20% 10% Interbank deposits Roll over 100% outflow 80% outflow Derivatives & contingent funding Roll over No roll‐over No roll‐over (Incl. FX swaps) Committed facilities provided No draw down No draw down 50% draw down Inflows Reverse repos = = = Retail & corporate Roll over No inflow 10% inflow Central bank Roll over Stable Stable Other Roll over 50% No inflow inflow Financial institutions Roll over No inflow 50% inflow Derivatives Roll over No roll‐over No roll‐over Others LCR adverse market + LCR 3 notch Derivatives No additional collateral downgrade posted Debt buy backs Amount reported in No No LCR CBC Cash Stable Stable Stable ECB eligible + Stable 95% 90% ECB eligible Stable 85% 80% Non‐ECB eligible Stable 50% 40% In the combined scenario, we assume that inflows and outflows will be impacted from first day on, and the counterbalancing capacity will also lose of its value progressively. Conversely, the 3 notch downgrade and the debt buy back will occur only after 6 months.

4.2.3. Outcome of our stress tests and way forward

4.2.3.1. The use of a stylised balance sheet as an input As we cannot use the individual data on banks, we will work on the basis of stylised balance sheets, taking inspiration in the proposal made by IMF in its paper on “Next Generation System‐wide liquidity Stress Testing”, and on some basic information we have on the structure of the banks’ balance sheet. We will differentiate between 3 types of banks:  Very large universal banks, which have traditional lending activities, but also some diversification in other areas like commercial and investment bank, trading, mergers and acquisitions, etc (typically, those banks have an average total balance sheet close to 1.5 Bn EUR).  Smaller banks without a specialised business model (typically 250 Mn EUR on the balance sheet). Those banks also have a diversified business model, even if the weight of market activities and commercial and investment bank is lower.  Smaller Banks with having a focus on asset management activities (typically 20 Mn EUR total balance sheet on average).

We present in the tables hereunder a picture of the contractual inflows and outflows on a 1M and 1 Y horizon for those various groups, divided by the total assets of those banks:

Universal Diversified Asset managers Outflows 1M 1Y 1M 1Y 1M 1Y Unsecured funding (ST & LT) 1.00% 5.00% 0.20% 2.00% 0.00% 0.00% Secured funding 0.00% 0.50% 0.00% 0.50% 0.00% 0.00% Repos 5.00% 8.00% 1.50% 2.00% 0.50% 0.50% Retail & corporate deposits Retail stable 1.00% 2.00% 8.00% 10.00% 0.00% 0.00% Retail unstable 0.50% 1.50% 8.00% 10.00% 0.10% 0.20% Corporate operational 1.00% 2.00% 1.50% 2.00% 0.00% 0.00% Corporate non‐ 1.00% 2.00% 3.00% 4.00% 0.10% 0.10% operational Central bank 2.00% 2.50% 0.00% 0.00% 12.00% 12.00% Other deposits 0.50% 1.00% 0.00% 1.00% 1.00% 5.00% Interbank deposits 1.00% 3.00% 1.00% 2.50% 16.00% 21.00% Derivatives & contingent 20.00% 50.00% 2.50% 7.00% 11.00% 60.00% funding Committed facilities provided (to financial 1.50% 0.50% 0.50%

institutions) Inflows Reverse repos 6.00% 8.00% 2.50% 3.00% 9.00% 11.00% Retail & corporate 2.00% 6.00% 1.50% 6.00% 0.50% 1.00% Central bank 2.00% 2.50% 0.00% 0.00% 12.00% 12.00% Other 0.50% 1.00% 0.00% 1.00% 1.00% 5.00% Financial institutions 1.00% 3.00% 1.00% 2.50% 16.00% 21.00% Derivatives 20.00% 50.00% 2.50% 7.00% 11.00% 60.00% Others Derivatives (adverse+ 4.00% 2.00% 1.00% collateral posted) 3 notch downgrade 0.70% 1.00% 0.00% Debt buy backs CBC Cash 0.10% 0.10% 0.50% 0.50% 0.00% 0.00% ECB eligible + 9.00% 10.00% 7.50% 6.00% 7.00% 7.00% ECB eligible 0.20% 0.20% 2.00% 1.50% 1.00% 1.00% Non‐ECB eligible 0.50% 0.50% 0.00% 0.00% 0.00% 0.00%

The amount of outflows and inflows is quite directly determined by the importance of the corresponding balance sheet items. A few points are worth being highlighted:  Derivatives explain a large chunk of cash flows, but inflows are close to compensating outflows. The observation is quite similar for repos and reverse repos, even if in absolute terms they have a lower impact on the cash flows.

 The bigger the bank, the more it relies on wholesale funding, whereas smaller banks rely more on deposits, and among them, on retail deposits. Asset managers rely largely more on interbank funding than the banks having a more diversified business model.  Larger banks tend to offer credit and liquidity lines to their financial counterparties (committed lines).  Asset managers have a smaller exposure to derivatives and therefore suffer less of the corresponding margin calls in case of a crisis. The composition of the counterbalancing capacity does change much, whatever the type of business model.

4.2.3.2. Detailed analysis of the stress tests So as to analyse the outcome of stress tests, the following steps should be taken:  calculate the net cash flow coverage ratio for each time bucket in each stress level  determine the counterbalancing capacity available  compare the forecasted need to the quantity of forecast funds available. It may also be interesting to estimate the time needed to get additional liquidity by selling the assets. The bank’s management and supervisors should analyse liquidity gaps per time bucket and time to illiquidity. The latter corresponds to the delay until the counterbalancing capacity would be exceeded by the net stressed outflows. It is a window of opportunity, as it tells the bank’s managers how long they would have to come up with additional cash in the event of a scenario like the one projected. The key questions to be answered with the stressed cash flow analysis are the following:  Is the bank covered? The analysis should spot any large or growing mismatches between funding needs and funding sources over time.  To what extent is the bank reliant on volatile or credit‐sensitive funding sources?  Is the liquidity reserve adequate?

4.2.3.2.1. The idiosyncratic scenario As the idiosyncratic scenario is rather short term, we will not present the cash flow analysis by time bucket. The impact of inflows and outflows is presented hereunder for the 4 types of business models. They are presented at an aggregated level. The reader can refer to the detailed figures displayed in annex 5:  Large universal bank:

Baseline Idiosyncratic Inflows 8.00% 28.00% Outflows ‐8.00% ‐26.66% Others 0.00% ‐0.70% Net stressed outflows 0.00% 0.64% CBC 10.80% 9.07% Gap 10.81% 9.71%

The main drivers for the idiosyncratic scenario are interbank deposits (‐1.2%), followed by the impact of the 3 notch downgrade (‐0.7%) and the outflow on corporate non‐operational deposits (‐0.30%). Inflows and outflows on derivatives and repos/reverse repos approximately compensate each other, their netted impact being positive. The net stress impact is positive, due to this mainly, whereas the baseline scenario was neutral.  Small diversified banks:

Baseline Idiosyncratic Inflows 3.00% 5.00% Outflows ‐2.00% ‐8.13% Others 0.00% ‐1.00% Net stressed outflows 1.00% ‐4.13% CBC 8.00% 9.33% Gap 9.00% 5.20% Patterns are completely different than for other types of business models: retail unstable deposits are the main source of outflow (‐1.5%), followed by interbank deposits (‐1.2%) and corporate non‐operational deposits (‐0.8%). The 3 notch downgrade also has a significant impact (‐0.8%). The net stressed outflows erase almost half of the counterbalancing capacity, whereas the baseline scenario was quite significantly positive (+1.00%).  Asset management banks:

Baseline Idiosyncratic Inflows 11.00% 32.00% Outflows ‐0.50% ‐27.75% Others 0.00% 0.00% Net stressed outflows 10.50% 4.25% CBC 8.00% 7.50% Gap 18.50% 11.75% Interbank deposits impact very negatively the net outflows (‐16%). It is significantly compensated by reverse repos (+9%) whereas outflows due to repos are rather neutral. The scenario erases almost 2 thirds of the counterbalancing capacity. None of the business models is short of liquidity under this stress scenario.

4.2.3.2.2. The combined scenario We summarise hereunder the outcome of the stress scenarios. The stressed gap is expressed as a percentage of the total balance sheet of the bank:

Stressed gap 30.00%

25.00%

20.00% Universal 15.00% Diversified 10.00% Asset management

5.00%

0.00% D1 D2 D3 D4 D5 D6 W1 W2 W3 W4 W5 M2 M3 M6 M9 Y1

The main drivers depend on the business models of the bank:  Universal bank: in decreasing order: derivatives (‐4%), unsecured funding (‐2.4%) and interbank deposits (‐2.4%)  Diversified bank: derivatives (‐2%), interbank deposits (‐1.8%), retail unstable deposits (‐1%), unsecured funding (‐1%)  Asset managers: interbank deposits (‐16%), other deposits (‐0.5%) and committed facilities provided (‐0.4%). Universal and diversified banks present quite similar patterns whereas asset managers present a very good resilience in case of a stress test. The time to illiquidity exceeds one year.

4.2.3.3. A few methodological challenges and possible refinements in the stress testing approach Some refinements may be introduced in the methodology, so as to acknowledge the complexity of the issue:  In large international groups, liquidity can be affected by local specificities. Firstly, liquidity can be trapped in some of the legal entities, due to constraints or limits affecting the free flow of liquidity. Those may result from internal rules or from the regulatory framework; moreover, different regulatory regimes may apply for different entities in the same group. As a consequence, access to liquidity may vary considerably, even in the same group. It is crucial to note that trapped liquidity increases in case of a crisis. Additionally, run‐off rates may differ among legal entities in a consolidated institution. The approach may be considered as being too rudimentary if one disregards those elements and omits the internal heterogeneities of a large group, event when reasoning on consolidated data. In addition, the stress testing may consider the currency composition of exposures or differentiate a bit more the haircuts based on the currency composition of the buffer of liquid assets.  The segmentation of time buckets is critical. A liquidity shortage inside a certain time bucket

might materialise but remain undetected in case the segmentation is not granular enough.  On a time horizon exceeding a few weeks, the bank can implement strategies to react to the crisis. The longer the time horizon is, the more difficult it is to neglect decisions taken by the bank. Therefore, one can consider incorporating behavioural reactions of the banks, in addition to its unstressed funding plan (which is only partially included in the input presented previously). Symmetrically, one may want to take into account the possible reaction of central banks and other public authorities. Taking into consideration the fact that some assets can be mobilised at the central bank is already a thing, but may not be sufficient. Anyway, neglecting those actions may be considered as quite conservative.  The modelling may incorporate the link between liquidity and solvency risks. Indeed, those are linked via various channels: in particular, funding costs and collateral needs increase with the rating and the solvency of the counterparty. It has even been established that there is a non‐linear relationship between solvency and funding costs for German and other European banks (Schmieder at al.). The impact of solvency on funding costs needs to be taken into account on longer time horizons.  Regulators who consider the banking system as a whole for the purpose of maintaining financial stability have a high interest at modelling 2nd round effects, or in other terms contagion effects and the issue of systemic liquidity. Indeed, the main issue with liquidity risk in a large and integrated financial system is the fact that exposures are correlated and there are financial interlinkages between banks. Van den End has proposed an approach to take this into account: o In the 1st round, the model simulates the effects of the scenario on the bank’s liquidity buffer. o 2nd round effects materialise if the bank takes mitigating actions of the bank. This may be the case if the net stressed outflow exceeds a certain level of the original buffer. Banks’ mitigating actions can have an impact on the bank itself, but also on other participants in the system. In particular, there is a higher probability that off‐balance sheet liquidity facilities are drawn or that banks will reduce their promised liquidity lines. Systemic risk becomes larger if more banks are touched, if reactions tend to be similar (herd behaviour) or if the reacting bank is larger or highly connected with the rest of the financial sector. This approach for modelling requires banks to provide their behavioural reactions for each of the scenarios, and to report also on their bilateral exposures and commitments.

4.2.3.4. Calibrating the counterbalancing capacity Stress tests may help the bank to analyse the dynamics of its balance sheet as regards liquidity risks. Nevertheless, the final purpose of the liquidity stress tests is ultimately to calibrate the size as well as the composition of the buffer of liquid assets. The required size and composition of the buffer are those that enable the bank to counterbalance possible liquidity gaps, the buffer itself being considered under stressed conditions. Those characteristics depend highly on the time horizon considered: the liquidity buffer should be composed of cash and core assets that are both central bank eligible and highly liquid in private markets. For the longer end of the buffer, a broader set of liquid assets may be appropriate, subject to the bank demonstrating the ability to generate liquidity from them under stress within the specified period of time. The conclusion of the analysis provided here above is that the liquidity buffers of the bank seem to be sufficient.

Highly liquid marketable assets should constitute the core of the buffer, but other assets which require a longer time to liquidate could be included in the buffer, which therefore would be available for the longer end of the survival period. The bank should demonstrate the ability to generate liquidity under stress from them within the specified time period of time. In particular, bank needs to have a clear understanding of the terms and conditions under which central banks may provide funding against eligible asset as collateral under stressed conditions. They should also seek to be active on a regular basis in each market in which they hold assets for liquidity purposes. This helps to reduce the stigma of firms suddenly becoming more active on markets, as this may alert other firms on the fact that they may be under liquidity pressure. Therefore, banks need to have well established platforms that allow them to raise more funds promptly. Last, but not least, the buffer should differentiate between currencies, and should reflect legal entity specificities where appropriate, especially with regard to intra‐group exposures. Determining the adequate location and size of the buffer should be responsive to individual needs and situations.

5. The specific issue of intra‐day liquidity risk

5.1. A subcategory of liquidity risk: intra‐day liquidity risk

5.1.1. Introduction Banks have to proceed to payments on a daily basis. They typically manage their payment flows so that they end the day flat, i.e. the value of incoming payments is roughly equal to the value of outgoing ones. The liquidity exposures that arise from payment and settlement activities are extinguished within a working day. Those exposures can be huge, in particular for settlement banks, i.e. banks which participate in payment systems on behalf of other banks. There is a risk that the bank is not able “to meet payment and settlement obligations on a timely manner under both normal and stressed conditions and contribute to the smooth functioning of payment and settlement systems.” (BCBS 2008). This is referred to as “intraday liquidity risk”. Intraday liquidity risk has been in the focus of banks and regulators in the last years, notably because it was dramatically illustrated with the failure of the Herstatt bank in 1974, and this fear was reactivated with the financial crisis. Herstatt was a German bank which was facing major difficulties which led the German banking regulator of the time to withdraw its banking license. German banks stopped their payments towards the bank, and it was soon not in a position any more to execute payments in Deutsche Mark. The bank was also bound to execute the USD leg of a large amount of FX swaps with American counterparties. Its correspondent bank in the US, Chase Manhattan, froze its account, so that it could not honour its commitments. They were in turn in great difficulty to execute payments in USD on the same day. In the context of the financial crisis, this risk has been very close to materialise on several occasions (Lehman Brothers was hardly able to execute margin calls before it went bankrupt). This is the reason why it has become a subject of concern for regulators and for the banking industry as well. This has contributed to enrich the reflexion on this topic and encouraged banks to monitor more closely this risk, to develop corresponding reporting tools and risk management frameworks. In intraday liquidity risk management, the issue of timing is crucial:  The banks shall be able to execute all payments by the end of the day. The bank may have the possibility to postpone some payments. One of the issues in this context may be to identify

those that can be postponed. Moreover, postponing too many payments may severely harm the reputation of the bank and lead to other types of risks.  There are issues related the intra‐day timing of payments. 2 constraints exist or may exist in this regard: there are payments considered as “critical” (see later) that should be realised before a given cut‐off hour; other payments designated as “residual” shall be realised later in the day. There may also be a throughput constraint in the system, i.e. a given percentage of payments should be realised before a given hour in the day. Even if there may be no strict constraint on throughput, it may still be closely monitored by regulators, payment systems and informally, by other stakeholders. We will elaborate on both challenges hereafter, but it is worth mentioning at this stage that in this regard, intraday liquidity risk raises the issue of simulating the timeline of events. It requires techniques that are used also for other topics, like forecasting the order in which an insurance company will have to reimburse some damages (.

5.1.2. The sources of uncertainty for intraday liquidity risk A distinction should be drawn between intraday liquidity risks which originate from the intraday payment or settlement processes and strategic liquidity risks which were originated before today. Strictly speaking, intraday liquidity risks are those that not only occur intraday but are also generated intraday; they cannot be anticipated on more than the daily horizon. Therefore, intraday liquidity risk corresponds to the very short term. We can provide here some examples of sources of intraday liquidity risk:  Some payments have been initiated previously but their materialisation has not been anticipated in the forward looking exposure. This would be the case if the information flow in the forward looking exposure system is inefficient or if a deal has been captured incorrectly, etc. This may also happen if the bank has not put in place a system sophisticated enough to capture all planned payments (in some cases, it is not worth investing in such systems given the perceived level of intraday liquidity risk). Last but not least, settlement banks have to realise payments on behalf of their client banks, which are not compelled or contractually forced to give notice for payments to be realised in the following days; this is a reason why settlement banks are usually more severely exposed to intraday liquidity risk.  Some payments have to be processed with a very short notice. This is for example the case for non‐financial transactions, for example payment of salaries or tax payments. Tax payments can be done on behalf of customers (for example, retail customers all pay their income tax on the same day), or for the bank itself. Those payments are usually processed by the responsible departments shortly before they are executed, and the operators in charge of managing intraday liquidity risk are informed last minute. Banks which are highly exposed to such types of payments may integrate them in their Forward looking exposure, based on past observations, and this may lead to the constitution of an intraday liquidity buffer for those days where such payments are anticipated. A residual exposure to Intraday liquidity risk remains, but associated with the uncertainty in the forecast.  Some deals are generated intraday or may contain options that might lead to intraday payments.  Additionally, margin calls because they are also known with a very short notice (usually within the same day).  Intraday liquidity risk may stem from payments that, although planned, have not been

received yet. For example, there may be a wilful non‐payment (breach of contract risk, operational risk). Counterparties may postpone or even cease payments to a smaller extent: counterparties may delay outgoing intraday payments while waiting for others to pay first. Uncertainty may stem from payments that have already been received. For example, a bank may not be aware that it has received a payment erroneously, and the counterparty may ask for reimbursement.  The bank may be at risk also due to its own incorrect payments, liquidity risk is here deriving from a form of operational risk. The payment has not been taken into account in the list of payments planned during the day.

5.1.3. How to manage intraday liquidity risk? Some basics As mentioned earlier, regulators have become increasingly worried about intra‐day liquidity risk in the last years. This has led BCBS to identify 6 operational elements for managing intraday liquidity. Those principles have globally become standards on how to manage intraday liquidity risk :  Banks shall measure expected daily gross liquidity inflows and outflows, anticipate the intraday timing of these flows and forecast the range of potential net liquidity shortfalls during the day. This is not only part of the regular intraday liquidity management, but is also necessary to forecast liquidity flows for the following days.  Banks shall monitor intraday liquidity positions against expected activities and available resources (balances, remaining intraday credit capacity, available collateral), i.e. they shall be able intraday on a continuous basis to forecast future payments and to check that they have sufficient liquidity to cover them, in whatever form.  They should arrange themselves to be able to acquire sufficient intraday liquidity to meet intraday objectives. This means in particular that they should manage and mobilise collateral as necessary to obtain intraday liquidity. They should also manage timing of liquidity outflows in line with intraday objectives.  They should put in place internal schedulers and a proper management of outflows. The internal scheduler consists in a projection of cash flows for the coming day. It is usually different from the forward looking exposure which corresponds to a longer time horizon and is maintained in a different IT system. The bank shall therefore develop an ability to forecast payments. This is relatively easy for payments that are generated internally before the given date. The challenge is higher for payments generated by clients in case of settlement banks: in this case, banks can ask their large clients to either pre‐position funds or give advance notice of large payments that need to be made on their behalf.  They should have sufficient liquidity buffers at their disposal. In the past, bank’s liquid assets requirements were not calibrated to include intraday liquidity risk. This constraint is currently better taken into consideration and banks now ensure that they have a liquidity buffer designed mainly at covering intraday liquidity risk. Some specific constraints appear in this case: in particular, it is essential that the liquidity can be made available very rapidly, i.e. before the end of the day. There may be an overlap between the intraday liquidity buffer and the “regular” liquidity buffer, we will elaborate later on how the bank shall manage this overlap. We provide hereunder a list of sources of intraday liquidity in decreasing order of

importance, as already listed by the Basel committee: o reserve (cash) balances readily available on the central bank account o collateral pledged with central banks that can be freely converted into cash via a liquidity line o other types of central bank credit lines o unencumbered assets on bank’s balance sheet that can be freely converted into intraday liquidity via money market. This can be done for example with repos o secured and unsecured funding sources available intraday from other banks (committed or uncommitted credit lines) o balances with other banks available for intraday settlement, payments received from other payment systems’ participants or through correspondent banking services. Those sources naturally add up to the payments that the bank will receive intraday, which can come from other large value payment systems participants, from ancillary systems and through correspondent banking services. In case of stress, it is not possible to rely on some of the liquidity sources: in particular unsecured funding may not be fully available. This shall be taken into consideration in a conservative manner. In particular, those funding sources shall be excluded from the computations under stress test scenarios. The intraday liquidity buffer is aimed at covering various sources of uncertainty. It shall therefore take various components into account: necessity to be able to cover anticipated, unanticipated or “critical” payments (see hereunder), ability also to face various stress scenarios. Some details on the calibration of the liquidity buffer will be provided later.  Banks need to have an historical database to calibrate the intraday liquidity buffer. For this purpose, they need to embed in their system a time stamp associated to each transaction. To tackle the issue of intraday liquidity risk, one should capture additional details, in particular, if payments are processed via third parties and if they are executed for clients. In case of payments via third parties (payment systems), there is a need to have information on execution deadlines. As mentioned earlier, it is much more difficult to anticipate in the strategic systems payments received from clients.  Reporting tools: the bank needs to analyse data on a regular basis and to put in place an adequate reporting. This is one of the regulatory requirements that have been put in place after the financial crisis. Here are some metrics to be reported by the bank:

o daily maximum intraday liquidity usage,

o largest positive/negative net cumulative position,

o available liquidity at the beginning of the business day (with some details on its composition),

o total credit lines available,

o total payments, total gross payments sent or received,

o total value of time‐specific obligations (This includes critical payments),

o intraday throughput at different hours in the day. Throughput measures the percentage of the total payments that have been realised for a given hour in the day.  Banks should put in place bilateral limits regarding intraday liquidity risk (limit the largest bilateral net debit position), both for counterparties in the payment system and customers for settlement banks.  Be prepared to deal with unexpected disruptions in intraday liquidity flows. One of the main objectives of intraday liquidity management is to ensure that the bank will be able to realise “critical” payments, as being those who could, if not settled:  generate disruptions in the global clearing system  threaten the participation in the global markets  originate reputational risk for the bank  or affect the bank by economic penalties Those are usually high value payments. They may not be realised on a daily basis, but only at given dates in the month. Therefore, they are associated with a critical day, as well as by a critical hour during the business day. As examples, we can mention SEPA settlement, CLS payment, payment to the custodian, margin calls with central clearing counterparties, retail system clearings. Settlement banks in the UK consider 4% of payments by value and 5% by volume to be critical. Based on our observations, the average amount would be closer to 10 %.Those payments that are not considered as critical are qualified as residual payments. Most of them can be postponed without any problem. The table hereunder summarizes the various types of uncertainties leading to intraday liquidity risk and the corresponding mitigation techniques:

Uncertainty / risk Mitigation

Deficiencies in the computation of the FLE Incorrectly captured deal, deficiency in the FLE Put in place internal controls to ensure that deals are appropriately flow, etc captured Have a liquidity buffer to face possible unanticipated payments Payments with very short notice Non‐financial transactions (ex: payment of The bank can create a dummy transaction in the system in advance, salaries or taxes) anticipating the upcoming amount. The day of the payment is known, and a corresponding reserve would be constituted. The level of the reserve can be determined based on historical data Deals generated intraday and having an Liquidity buffer. The day of the payment and its amount are both intraday cash effect / intraday short payment unknown. options Margin calls Margin calls are critical payments The day and even the hour of the payment are known. The amount may be significant, it is quite volatile. The bank can constitute a dedicated liquidity reserve. It can be calibrated based on the computations done in the context of counterparty risk management. Uncertainty about planned incoming payment or about payments already received Counterparty cancelling or postponing Liquidity buffer. This is a risk with a large impact, but a low probability payment occurrence At system‐wide level, put in place constraints as regards the timing of

payments (throughput) The bank has received a payment erroneously Internal controls should ensure that the bank is able to detect erroneous payments Error on the bank’s side The bank sends the payment to the wrong The bank should put in place strong internal controls to avoid such beneficiary. There is some uncertainty on the errors correction of the error by the end of the day

We have tried to develop hereunder a more detailed taxonomy of payments, based on their level of uncertainty:

Existence known in Amount known in Payment to be executed advance advance at a given hour

Non‐financial payments x

Critical payments (Margin calls x x

Not on a individual basis, Some of the payments Payments realised on behalf of a but on the total portfolio can be anticipated if client if the bank acts as a of clients, payments will there is prior notification settlement bank surely need to be done from the client

Not on a individual basis, Some of the payments Payment on behalf of a client but on the total portfolio can be anticipated if

(not acting as a settlement bank) of clients, payments will there is prior notification surely need to be done from the client

5.2. How to calibrate the liquidity buffer to cover intraday liquidity risk As mentioned earlier, it is essential to dispose of a sufficient liquidity buffer to cover the various types of uncertainties associated with intraday liquidity risk. We aim here at defining an approach for this, under normal and stressed conditions. We will analyse first how we can extend the Fiedler framework to intraday payments; based on this, we will present the tool that we have developed to simulate the execution of the payments. We will then explore the conditions of the convergence of the simulator, present the necessary reserve under different hypotheses, and present some sensitivity analysis.

5.2.1. A framework to perform simulations: extending the Fiedler approach to intraday payments It is possible to analyse intraday liquidity risk in the framework defined by Robert Fielder. As necessary under this approach, it is possible forecast future payments on the intra‐day horizon, with the main specificity that intra‐day liquidity management focusses on the last moment before cash flows are converted into payments, and that the bank has less options to react to a liquidity shortage. At the beginning of the day, banks do their best to forecast upcoming payments, and check if they will be able to honour their commitments, in particular as regards critical payments. Similarly to the

61 longer time horizon, part of the cash flows are known in advance. They may be initiated 1, 2 or 3 days before they are executed (this corresponds to the notion of value date: there is a delay between the moment the payment is initiated and the moment it is executed). Nevertheless, as mentioned earlier, there remains a part of uncertainty, which is due either to the bank’s actions or to decisions taken by counterparties, or simply to hazard. The bank is aware that some payments are anticipated, but may not be realised, whether incoming or outgoing, and that some payments are unanticipated. As mentioned earlier, the issue of timing plays a very specific role, in particular with critical as opposed to non‐critical payments. This is also the case with the computation of the forward looking exposure, but on the longer term, the bank has more options to adjust its strategy and honour its payments. As compared to the longer time horizon, the bank has to react in the very short term (before the end of the day) and only has few options to react: cancel or postpone payments and or use the liquidity reserve. In case there are unanticipated payments to be realised, the bank has to adjust the timing of payments, which means that new information shall be integrated and corrective actions shall be taken immediately. Expected cash flows shall be continuously recomputed to incorporate the effect of new transactions and not only at the end of the day. This requires some methodological adjustments as compared to what was presented for the forward looking exposure. In case the bank realises at a given moment in the day that it does not hold enough liquidity to face its obligations and the respective cut‐off dates, it will try to postpone part of the outgoing payments, hopping that some unanticipated payments will restore the liquidity buffers. If we use the concepts introduced with the Fiedler methodology, we should have at any time: 0 (1) where t < 1 day

If we denote and the number of outgoing and incoming payments and and each of the outgoing and incoming payments, we have:

And ∑ ∑ We will later in the thesis distinguish between various categories of payments, and introduce various approaches to manage the risk. This will reduce or increase the number of constraints on the forward looking exposure and the counterbalancing capacity. As compared to what may be done on a longer time horizon, the only parameter that the bank can influence is the timing of outgoing payments. We can denote it: ,,…, where N is the total number of outgoing payments. This is the input of the simulation. The bank may anticipate some payments and postpone some others so as to respect the constraint set by equation (1) and so as to realise payments as early as possible – critical payments are excluded from this. The output of the simulation is the adjusted sequence of outgoing payments , ,…,

5.2.2. How to calibrate the level of the liquidity buffer At the beginning of the day, the bank shall have ensured to have sufficient resources to execute its critical and residual payments. Executing residual payments is a secondary objective: some of those payments can be postponed.  Executing critical payments in due time is the primary objective of intraday liquidity management.

As mentioned earlier, the impact of not executing a critical payment would be extremely serious. Therefore, the bank shall ensure at any moment of the day that it disposes of a sufficient amount of highly liquid assets. The amount of this buffer shall be calibrated conservatively enough. To do so, one approach would be the following:

o The bank shall identify the various types of critical payment. It shall identify which is the hour where they shall be executed. It shall then collect historical series on a long time horizon with the amount of such payments.

o The bank shall then estimate the distribution of each critical payment. This may be done for example by computing an historical VaR, but other approaches can be considered.

o The bank shall then sum up each contribution in order to calculate the potential maximum exposure related to critical payments. To cover critical payments, the bank shall dispose of adequate sources of liquidity, in the present case very liquid ones: this includes in particular the cash position of the bank, the credit line available at the central bank and the amount corresponding to the collateral that is pledged at the central bank and can easily be converted into a credit line. Collateral held in ancillary systems may also be considered as sufficiently liquid to cover intraday liquidity risk.  Executing residual payments is a secondary objective. The bank shall dispose of a buffer of liquid assets that will be sufficient both on the amount but also regarding its composition to be able to execute residual payments. To do so, the bank shall also analyse the data history of residual payments and derive a distribution from it; the liquidity buffer can be calibrated on the basis of an historical VaR, but other methodologies may also be considered. The main difference with critical payments resides here in the fact that residual payments are, on average, of a lower amount, but that they are also much more numerous. Liquidity sources can be a bit less liquid than for critical payments: the corresponding reserve may include the liquidity sources that we have already mentioned, as well as additional types of assets, for example the counterbalancing capacity, taking into consideration assets that are accepted not only by central banks but also by a larger set of market counterparties. The issue may be raised whether the bank may take into consideration incoming payments when calibrating its liquidity buffer. Indeed, incoming payments balance on average outgoing payments, and the bank shall decide to which extent it may consider them as a liquidity source in case of need. One possible approach would be to take a very conservative stance on critical payments, and consider that they should be executed even if there is an incident that would block the execution of incoming payments, and being a bit less conservative on residual payments, therefore taking the corresponding incoming payments into account.

5.3. Some simulations

5.3.1. Specification of the model We will describe hereafter the “automat” that we have developed to simulate the daily execution of payments and the way the banks manage the queue of outgoing payments taking into account their nature, the incoming payments and the level of the various reserves held. The model is calibrated in general on the basis of public information. Nevertheless the different parameters can be adjusted to test the model.

There are 2 steps in the approach:  Firstly, we will generate the list of payments that the bank will have to manage during the day.  Secondly, the tool will manage the queue of payments to be executed, applying a set of predefined rules. Both steps are fully independent, and it would possible to execute the second step with utilising a database of payments provided by a bank and based on this to calibrate the liquidity buffers.

5.3.1.1. Generating payments We will rely on a very simple taxonomy of payments: we distinguish critical from residual payments, and among residual payments, we only separate those that are anticipated from those that are not. We consider that day begins at 9 am and closes at 5 pm. Time step is set at 15 mn.  Outflows: There is a difference between residual payments and critical payments

o Number: The number of critical payments is ensured, there is one critical payment per critical hour. We generate residual payments considering that the number of payments follows a Poisson distribution. This distribution may be calibrated based on observed data. To facilitate our computations, we have set the parameter at the same level for incoming and outgoing payments. We do not introduce any distinction between the various types of residual payments, apart from the fact that some of them are unanticipated.

o Amount: the amount of critical payment follows a normal distribution, the same type of distribution being used for the critical of payments. Similarly, the amount of residual payments follows the same distribution, whatever the type of residual payments. We will test two types of distributions, to explore the impact on the level of the intraday liquidity reserve. This aspect of the model could be fine‐tuned if necessary, we could for example introduce different categories of residual payments. The mean and standard deviation of each critical payment differ, as well as for residual payments.

o Timing: the timing of critical payments is known in advance. The timing of the other types of payment is determined with the assumption that they are uniformly distributed in the day. As a refinement, it would be possible to specify another distribution.

o When generating payments, we flag among the residual payments which ones are unanticipated, using a Bernoulli distribution. The percentage of unanticipated payments is one of the parameters in the model.  Inflows. We will generate inflows only for residual payments. We may disregard any possibility to compensate critical outflows with critical inflows or not. The approach will be different for residual payments, where we the number and payments and counterparties is much higher, and the chances of a large shortage of incoming payments are lower. For those we will take into account the netting between incoming and outgoing payments. The process for generating outflows is similar to the one implemented for inflows, as regards the number of payments, their distribution and the percentage of unanticipated payments.  Calibrating the liquidity buffer. The level of the liquidity buffer is known at the beginning of the day. It is split between the buffer aimed at covering critical payments, the buffer aimed at covering residual unanticipated payments and the buffer for residual anticipated payments.

In the latter case, the amount of the liquidity buffer is calibrated only at the beginning of the day. In case the bank knows that the amount of incoming payments exceeds the amount of outgoing payments, it would not set aside any liquidity reserve for anticipated payments. Conversely, it will constitute a liquidity reserve only if it anticipated that incoming payments will not compensate outgoing payments. Anticipating as many payments as possible helps reduce the level of the liquidity reserve, as we will confirm with our calculations later. We will work on the following assumptions:  On average, the amount of incoming payments equals the amount of outgoing payments; this corresponds to a situation that is manageable for the bank and that corresponds to what banks usually observe.  The average number of incoming payments equals the average number of outgoing payments.  The characteristics of the distributions of payments will be similar (same type of distribution, same mean, same standard deviation for, respectively, critical and residual payments)  Depending on the complexity of the simulation to be performed, we will test a number of payments that will be close to what can be observed in a large bank (10 000 per day) or a bit lower.  Critical payments will represent 1/10 of the amount of total payments. This exceeds slightly the figures mentioned earlier but corresponds to the data we have collected.

5.3.1.2. Executing payments The model will simulate the behaviour of an operator who has to manage intraday liquidity for a bank. He begins the day aiming at realising all outgoing payments during the day as early as possible. He will execute payments as they come, but with the constraint of maintaining some liquidity reserves above a given amount. His way of reasoning will be the following:  At the beginning of the day, he is able to anticipate a portion of the outgoing and incoming payments. He ensures at the beginning of the day that the difference is readily available on the central bank account, in the form of a reserve for anticipated payments. When the day begins, he will process as many anticipated and unanticipated outgoing payments as possible as early as possible, as long as the amount of the respective liquidity reserves remains positive. The incoming payments will come in due time.

Let’s denote , ,…, the hours where the outgoing payments are supposed to be executed and , ,…, the hours of the incoming payments. The bank will first realise all outgoing payments at the beginning of the day ( as long as 0 (1) Later in the day, the bank will maintain the hours of the anticipated payments as long as this inequality holds true, i.e.:

0 (1)

If j is defined by /

 When the liquidity reserves have been fully used, namely as soon as inequality (1) does not

hold true anymore, the operator will have to wait for future incoming payments. It will postpone outgoing payments until then. When incoming payments arrive, the operator will execute first the largest outgoing payments, postponing the others until the next incoming payments.  He also knows he will have to keep a reserve to proceed to critical payments. Their timing is known, but their amount not. He shall preserve the full amount or part of the amount of the reserve for critical payments until the critical hour, i.e. the moment where all critical payments will have been realised. As soon as some of the critical payments are realised, he may use the residual amount of the reserve for other purposes. We will consider in the first step that the 3 reserves held throughout the day ‐ the reserve for anticipated payments, the reserve for critical payments and the reserve for residual payments ‐ are independent. Incoming payments, depending on their nature, are added to the corresponding reserve. We will later consider other approaches. In the model, as soon as it appears that one of the critical payments cannot be executed during the day, the day is registered as a critical fail; if some of the payments cannot be executing during the opening hours of the payment system, the amount of payment not executed is registered. We will also record the amount of outgoing payments realised before a given hour of the day (The throughput): this will enable us to measure the impact of changing some of the rules described here above. As regards the If we formulate the constraints of the model with a more formalistic approach:

 we calibrate first the reserve for critical payments ( so that it is equal to the quantile of the total amount of critical payments for percentage :

∑ ) where is the number of critical payments. We do not consider here the possible netting effect between outgoing and incoming critical payments. In our model, critical payments have the same normal distribution with mean m and standard deviation . The sum of critical payments will therefore have a normal

distribution of mean and standard deviation .  We calibrate the reserve for anticipated residual payments so that:

∑ ∑ , 0) if we count incoming payments as being positive and outgoing payments as being negative.  If we consider each reserve as being independently as regards their use (i.e. the reserve for critical payments cannot be used to cover residual payments), we calibrate the reserve for unanticipated residual payments so that:

∑ ∑ ), being the quantile of the distribution for probability β. It is worth highlighting that the reserves are calibrated based on the distribution of payments, which is different from what we did on a longer time horizon where it was scenario based.

5.3.1.3. Some tests on the model / sensitivity analysis

5.3.1.3.1. Tests on the convergence of the model We will first test the convergence of the model with a varying average number of daily payments. All other things remaining equal, we will test hypotheses where there are between 50 and 10 000 payments on average per day. The latter hypothesis corresponds to a realistic number of payments for a large bank. The total average amount of both incoming and outgoing payments remains equal to 1 bn EUR. Therefore, the average amount of each payment decreases when their number increases. We assess, for each number of payments, the reserve that is necessary to cover outgoing payments in at least 95% of the cases, and the dispersion of those estimations depending on the number of simulations. We take at this stage the assumption that payments follow a Gaussian distribution. This is summarised in the graphs hereunder (we produce 10 estimations for each number of simulations). The red line corresponds to the estimated reserve for a very high number of simulations, i.e. 500 000. Horizontally, we display the number of simulations, and vertically the outcome of the simulation (in MEUR). It should be noted that some of the blue points may overlap. We kept the same scale for the vertical axis so as to be able to compare the efficiency of the convergence.

50 payments 1 000 payments 244 58 243 57 242 56 241 55 240 54 239 53 238 52 237 51 236 50 235 49 234 48 0 10000 20000 30000 40000 50000 60000 0 10000 20000 30000 40000 50000 60000

2 000 payments 5 000 payments 44 28.3 43 27.3 42 26.3 41 25.3 40 24.3 39 23.3 38 22.3 37 21.3 36 20.3 35 19.3 34 18.3 0 10000 20000 30000 40000 50000 60000 0 10000 20000 30000 40000 50000 60000

10 000 payments 22 21 20 19 18 17 16 15 14 13 12 0 10000 20000 30000 40000 50000 60000

Once we exceed 20 000 simulations, convergence becomes good, whatever the number of payments. For a given number of simulations, convergence improves with the number of payments. This makes sense, as increasing the number of payments reduces the variance of their sum (the chance is higher that large payments will compensate smaller payments. As we know from experience that the number of payments in large banks will be close to 10 000, we will focus in our simulations on this assumption, using 50 000 simulations to calibrate the size of the reserve for unanticipated payments.

5.3.1.3.2. Impact of the number of payments on the size of the reserve Relying on 50 000 simulations, we test the evolution of the reserve for anticipated payments when the number of payments increases. The outcome is the following:

Reserve for unanticipated Number payments (in MEUR) 50 239.4 500 74.6 1 000 53.0 2 000 39.0 5 000 23.3 10 000 17.0 The size of the reserve for unanticipated payments decreases when the number of payments increases. This can be explained easily based on the behaviour of the variance of the total amount of payments when the average number of payments increases. Indeed, we now that:

Where N follows a Poisson law with parameter λ and Pi , designating the value of payment number i, follows a normal law. Then, we know that:

/ / Assuming that the amount of the respective payments are independent, we derive the following equation:

Thus :

λ∗Var We have calibrated the number of payments and their individual average and standard deviation so that :

/4 It is also quite easy to demonstrate that:

λE In our model, E(P) is constant, whatever the average number of payments

Therefore : 17 17 λ∗ ∗ ∗ 16 λ 16 It results that the variance of the total amount of payments decreases with the average of their number, which is in line with our simulations. This means that the higher the number of payments the bank receives for a total amount of payments remaining constant, the lower the size of the corresponding reserve as compared to the average total amount received.

5.3.1.3.3. Changing the type of distribution of individual payments We also tried to compare the hypothesis where residual payments would individually follow a Gaussian distribution with the other hypothesis where payments would follow a gamma distribution. Indeed, it seems that the gamma distribution corresponds empirically better to the distribution of payments in banks: the queue of the distribution is thicker than the one of the Gaussian distribution, but there is also a higher probability of receiving payments with a lower amount. Average and standard deviation of both distributions are similar: they amount respectively to 100 000 EUR and 25 000 EUR. Under this assumption, with 10 000 payments on average per day and 50 000 simulations, our simulations lead to a necessary reserve that would be close to the one necessary with a Gaussian distribution, i.e. 17.0 MEUR. This is also quite understandable for 2 reasons:  The number of payments follows a Poisson law, which is quite concentrated around its average. Working on the assumption that the number of daily payments would be fixed, the total amount of payments per day would be equal to the sum of a deterministic number of independent payments that follow the same distribution. This complies with the conditions of the central limit theorem that stipulates that this sum tends in probability and almost surely towards the Gaussian distribution when the number of variables summed up approaches infinity. It results in this case that the total amount of daily payments would be close to a Gaussian distribution when the number of daily payments would be high. The standard deviation of this distribution would equal to √λ √

Thus:

It is worth noting that this equals to the variance computed earlier minus . We derived the level of the reserve for unanticipated payments under this condition, and we compared it with the result of our simulations:

Comparison Simulations vs CLT 300

250

200

150 Simulated Theoretical CLT 100

0 50 1000 2000 5000 10000

Our simulation with a probabilistic number of payments leads to a higher reserve, this is quite understandable as well, as the corresponding distribution has a higher standard deviation (the randomness of the number of payments introducing more variability). It appears also that both computations tend to converge and that they both trend to zero. This would be due to the fact that when the average number of payments increase, the total amount of daily payments would tend to follow a normal distribution, whatever the shape of the distribution followed by individual payments. The summing of payments would narrow the differences between the individual distributions.

5.3.1.3.4. Impact of the proportion of unanticipated payments on the calibration of the reserve for residual payments We revert to the assumption that the amount of payments follows a Gaussian distribution and we test the impact of anticipating a larger or a smaller share of payments. Indeed, being unable to anticipate the amount of incoming payments increases uncertainty and the amount of the reserves to be held to cover the possible intraday gap. As regards anticipated payments, the gap is known at the beginning of the day and the amount of liquidity reserves is optimal in the sense that it covers exactly the intraday needs. On the contrary, reserves for unanticipated flows are calibrated to cover a given quantile of the corresponding gap: on purpose, it shall exceed almost systematically the gap observed ex‐post. If we simulate a situation where there 10 000 payments are expected for the upcoming day, we compute the total amount of reserves for anticipated and unanticipated payments under 2 extreme scenarios which are the case where all payments can be anticipated, or the case where they cannot be anticipated at all. The reserve for anticipated payments is set at the beginning of the day, the reserve for unanticipated payments is determined at a level for which the intraday gap will be covered in 95% of the cases. We present hereunder the outcome, in the case of 50 000 simulations of the necessary level of reserves. The level of the reserve for anticipated flows corresponds to the average of the reserve that should be constituted at the beginning of the day. The level of the reserve for unanticipated flows is fixed and based on the 95% threshold:

(MEUR) Reserve for anticipated Reserve for unanticipated Total payments (average) payments No payment can be 0 24.3 24.3 anticipated Half of the payments 4.1 17.0 21.1 can be anticipated All payments can be 5.8 0 5.8 anticipated

The total reserve decreases dramatically if a larger portion of the payments can be anticipated. Nevertheless, the reader should be aware that anticipating a large share of their payments is a complex issue as well as a challenge for banks. As mentioned earlier, it requires them to put in place adequate processes and IT systems to do so; the lowering of the reserve requirement may not always be an sufficient incentive to realise the investments that are necessary for this purpose.

5.3.1.3.5. Using the reserve for critical payments to cover the gap resulting from residual payments We use here the assumption that all payments have a normal distribution and that half of the residual payments are anticipated. There are 4 critical payments per day and on average 10 000 critical payments per day. The average total amount of critical payments represents 1/10 of the average total amount of residual payments (100 MEUR vs 1GEUR). The reserve for critical payments may be constituted to cover either the gross amount of outgoing critical payments or their net amount. In the latter scenario, the bank will most probably fail to execute its critical payments if she does not receive one of the incoming critical payments. We will explore this case when elaborating on stress scenarios. We will focus here on the hypothesis where the reserve covers the gross amount of critical payments. Once the 4 critical payments have been executed, the residual reserve can be used to realise the non‐critical payments. We will compute the total reserve (critical + residual) corresponding to the 99% threshold for critical payments and to the 95% threshold for residual payments under 3 scenarios:  Scenario 1: the 3 reserves are segregated.  Scenario 2: the reserves for critical payments and for residual payments are segregated, but the residual reserve for anticipated payments can be used to execute unanticipated payments when all anticipated payments have been done.  Scenario 3: the residual reserves for critical payments and for anticipated non‐critical payments can be used to execute unanticipated non‐critical payments once critical payments have been totally realised. We exclude the use of the reserve for critical payments to cover anticipated payments, as this would not correspond to the mechanics of the execution of anticipated payments (they are deterministic, and the corresponding reserve as well; doing so would introduce some uncertainty in the management of anticipated payments).

Reserve for critical payments covering gross Reserve for critical payments covering net outflows outflows In MEUR Scenario2 Scenario 3 Scenario 2 Scenario 1 Reserves Scenario 1 Scenario 3 Reserves Reserves Reserves critical & Reserves Reserves completely critical & fungible residual fungible segregated segregated residual segregated segregated Reserve for critical 129.1 129.1 129.1 29.1 29.1 29.1 payments Average reserve for residual payments 4.2 4.2 4.2 4.2 4.2 4.2 anticipated Reserve for residual 0 14.9 16.8 0.0 14.9 16.8 payments unanticipated Average total reserve 133.3 148.2 150.1 33.3 48.2 50.1 Average end of day 133.6 148.7 150.6 29.7 49.7 50.4 balance It is not necessary to constitute reserves for unanticipated non critical payments in both configurations when the reserve for critical payments can be used to execute residual payments. The amounts at stake for critical payments and their uncertainty are much higher: this necessitates constituting a reserve that largely covers also in most of the cases the uncertainty attached to residual payments (which is much lower). Covering only the net critical outflows helps to reduce considerably the reserve to be constituted at the beginning of the day, but if there is an incident on one of the critical incoming payment, the probability is high that the bank will not be able to execute its critical payments.

5.3.1.3.6. Tests on the throughput We tested the impact of various levels of reserves on throughput, throughput being defined as the amount of payments being executed before 3 pm on the total amount of payments realised, in case all critical payments are executed and no residual payments need to be postponed until the following day. We test various approaches as regards the priorities applied by the bank when processing payments (largest payments in the queue being executed first or smallest payments having priority). The outcome of those simulations is presented hereunder. As previously, the buffer for anticipated payments varies from one simulation to another, and we will present in the table the average of the buffer for anticipated payments. The distribution of individual payments is normal. We also test the alternative approach where the distribution of payments follows the gamma law. We assume that there are 500 payments per day (due to constraints linked with our computation resources) and that the reserves are managed separately.

Size of the reserve for Average size of the reserve Rule for managing the Type of anticipated payments for anticipated payments queue of outgoing distribution Throughput (in MEUR) (in MEUR) payments 75 18.9 Largest payments first Normal 77.5% 100 68.9 Largest payments first Normal 82.1% 200 100.3 Largest payments first Normal 84.4% 75 18.9 Smallest payments first Normal 77.5% 200 100.2 Largest payments first Gamma 84.4% Based on this, we can draw the following conclusions:  The marginal impact on the throughput of increasing the size of the liquidity buffer decreases.  Changing the rule regarding the order according to which payments are realised depending on their amount does not have any impact on the throughput  Even with simulating only 500 daily payments the throughput is not affected by a change in the distribution of individual payments.

5.4. Stress testing intraday liquidity risk According to case studies provided by BIS, collateralisation of intraday credit and other exposures of payment and settlement banks to the stressed firm is a major source of liquidity risk. Some settlement banks increased their collateral requirements in case of a crisis. In case of a stressed situation, banks have an incentive to delay intraday outgoing payments while waiting for others to pay first. BCBCS identified 4 stressed scenarios for intraday liquidity risk:

 Financial stress: counterparties defer payments or withdraw intraday credit lines. This scenario may impact banks that are highly dependent on incoming payments.

 Counterparty stress: the bank cannot rely any more on the payments coming from one stressed counterparty.

 Customer bank’s stress: other banks defer payments to the customer of the bank (correspondent banking services or settlement bank). Banks that offer correspondent banking services normally advance intraday liquidity credit to their financial institution customers. Intraday credit lines that settlement banks extend to their customers are typically uncollateralised. Based on our observations, payments on behalf of correspondent banking customers represent 5% of the total.

 Market‐wide stress: this scenario has an impact on the value of liquid assets and higher haircuts should be applied to liquid assets. In a worst case scenario, some assets would simply be excluded from the intraday liquidity buffer after a downgrade. Integrating this into our framework would necessitate further developments. We would suggest the following approach:  Financial stress: we would reduce the number of incoming payments (e.g by 20%) and modify their distribution throughout the day (so that on average they would come later in the day)  Counterparty stress: we would need to identify the largest counterparty of the bank (excluding critical payments) and delete them from the database of incoming payments  Customer bank’s stress: Given the global proportion of payments done for customers, we

would decrease incoming payments by 5%.  Market‐wide stress: we would introduce a haircut on the liquid buffer. Additionally, one may introduce some kind of correlation between payments.

5.5. Ensuring consistency in the use of the liquidity buffer to cover intraday liquidity risk and longer term risks Banks can use their liquidity buffers to cover intraday liquidity risk as well as liquidity risk on a longer time horizon ; there is a risk associated with this double use of the liquidity buffer (e.g. Lehman used the assets held to ensure balance sheet resilience to cover intraday liquidity risk). In most of the jurisdictions, institutions are nevertheless authorised to leverage the liquid assets used in their LCR calculation within their daily intraday liquidity management framework. Under the assumption that outgoing payments are more or less compensated by incoming payments, many regulators think that even if the bank begins to tap the intraday liquidity buffer during the day, it will be more or less replenished at the end of it. This does not work in a period of prolonged stress test which will begin to eat the prudential asset buffer; therefore, the assets intended to cover longer term risk may be already pledged at the central bank or into the payment systems. One solution would be to ask a bank to calibrate their liquidity buffers to include intraday liquidity risk as a separate risk driver, which would be a quite radical solution when the bank is not going through a difficult period. At least, it should be expected from treasurers that they would maintain a broad understanding of the liquidity usage in order to strategically coordinate the interplay between intra‐day liquidity risk and longer term liquidity risk, and that they would be willing to isolate more drastically both buffers in case it becomes necessary.

6. Conclusion There is a continuum in the management of liquidity between the very short term (intraday liquidity) and the long term that is represented by the use of similar techniques to forecast future incoming and outgoing payments and by the common concept of the counterbalancing capacity which may be used on the full time horizon. This explains why bank usually do not completely segregate the buffer of liquid assets used for intraday liquidity management or for other purposes. Nevertheless, the main issues for managing risk and the corresponding methodological choices to measure the risk may diverge significantly. In the context of intraday liquidity, operators only have very limited time to react to emerging risks in case of emergency: the main challenge here is to adjust on an ongoing basis the timeline of payments so as to maintain at any moment a positive amount on the nostro account. Many other options are available on the longer term. Calibrating the liquidity reserve is only one of the many requirements for a bank to appropriately manage its liquidity risk. In this context, we have focussed for intraday liquidity risk under regular liquidity conditions, as this is an area where banks are still developing methodologies. Our simulations provide us some hints as to how banks shall optimise the calibration of their liquidity buffers: they should aim at covering gross critical outflows, as the amount of the reserve for residual payments is much lower, they should try as much as possible to anticipate the amount of future payments. Above a given number of payments, their individual distribution has a minor impact and the level of the overall reserve can

74 also be lower. The throughput depends highly on the amount of reserves, but with a decreasing marginal impact. Stress tests should also play a major role in this regard, even if most of the banks still have some work to do in this regard. Managing liquidity risk on a longer time horizon is a topic that was explored much earlier by practitioners and academics, even though the recent liquidity crisis has changed perspectives a bit. It has led banks and supervisors to increase their standards significantly as regards IT systems, monitoring, managing and reporting. The crisis has revealed, if still necessary, the binary nature of liquidity risk and the central role played by stress tests. Techniques for calibrating the liquidity buffers vary significantly between the very short term and the longer term. On the shorter time horizon, the main uncertainty concerns the timing of residual payments that may change very quickly depend on circumstances whereas the amount of payments is an issue mainly for critical payments. The timing of those is known in advance. Anyway, behavioural assumptions have a minor role to play and the level of the liquidity buffer and the latter can be calibrated based on past observations as regards both the existence, timing and amount of past payments; it is not so useful to understand what drives payments that impact the nostro account. On the longer time horizon, it becomes much more critical to take into account environmental information (like interest rates, evolution of the monetary policy, of the macro‐ economical environment) and the possible reactions of customers. It requires both different data and different modelling techniques.

Annex 1 : the ECB supervisory maturity ladder

Code ID Item

010-550 1 OUTFLOWS

010 1.1 Liabilities resulting from securities issued 020 1.1.1 unsecured bonds due 030 1.1.2 hybrid bonds due 040 1.1.3 bonds eligible for the treatment set out in Article 129(4) or (5) of CRR due 050 1.1.4 bonds as defined in Article 52(4) of Directive 2009/65/EC other than those reported to in item 1.1.3 060 1.1.5 securitisations due 070 1.1.6 short-term paper due 080 1.1.7 of which to intragroup entities 090 1.1.8 of which debt securities issued for retail only 100 1.2 Liabilities from secured lending and capital market driven transactions as defined in Article 192 of CRR, collateralised by: 110 1.2.1 Central Bank eligible assets 120 1.2.1.1 securities with a 0% risk weight 130 1.2.1.2 securities with a 20% risk weight 140 1.2.1.3 bonds eligible for the treatment set out in Article 129(4) or (5) of CRR 150 1.2.1.3.1 credit quality step 1 160 1.2.1.3.2 credit quality step 2 170 1.2.1.3.3 credit quality step 3 180 1.2.1.4 bonds as defined in Article 52(4) of Directive 2009/65/EC other than those reported to in item 1.2.1.3 190 1.2.1.4.1 credit quality step 1 200 1.2.1.4.2 credit quality step 2 210 1.2.1.4.3 credit quality step 3 220 1.2.1.5 non financial corporate bonds 230 1.2.1.5.1 credit quality step 1

240 1.2.1.5.2 credit quality step 2 250 1.2.1.5.3 credit quality step 3 260 1.2.1.6 residential mortgage backed securities of credit quality step 1 270 1.2.1.7 other assets 280 1.2.1.8 of which central bank open market operations 290 1.2.2 non-central bank eligible but tradable assets 300 1.2.2.1 equities listed on a recognised exchange, not self issued or issued by financial institutions 310 1.2.2.2 gold 320 1.2.2.3 other assets 330 1.2.3 of which to intragroup entities 340 1.3 Liabilities not reported in 1.2, resulting from deposits by customers that are not financial customers 350 1.3.1 by retail customers 360 1.3.2 by non-financial corporate customers 370 1.3.2.1 of which are intragroup entities 380 1.3.3 by are central banks 390 1.3.4 by other entities 400 1.3.4.1 of which are intragroup entities 410 1.3.4.2 of which are public sector entities 420 1.4 Liabilities not reported in 1.2, resulting from deposits by customers that are financial customers 430 1.4.1 by credit institutions 440 1.4.1.1 of which are intragroup entities 450 1.4.2 by financial customers other than credit institutions 460 1.4.2.1 of which are intragroup entities 470 1.4.3 of which are members of an institutional network 480 1.4.3.1 of which are intragroup entities 490 1.5 FX-swaps maturing 500 1.6 Amount payable from the contracts listed in Annex II of CRR other than those reported in item 1.5 510 1.7 Other cash-outflows 520 1.7.1 of which to intragroup entities 530 1.8 Of which: Interest flows due 540 1.8.1 of which to intragroup entities

550 1.9 Total outflows

560-1030 2 INFLOWS

560 2.1 Monies due from secured lending and capital market driven transactions as defined in Article 192 of CRR, collateralised by: 570 2.1.1 Central Bank eligible assets 580 2.1.1.1 securities with a 0% risk weight 590 2.1.1.2 securities with a 20% risk weight 600 2.1.1.3 bonds eligible for the treatment set out in Article 129(4) or (5) of CRR 610 2.1.1.3.1 credit quality step 1 620 2.1.1.3.2 credit quality step 2 630 2.1.1.3.3 credit quality step 3 640 2.1.1.4 bonds as defined in Article 52(4) of Directive 2009/65/EC other than those reported to in item 2.1.1.3 650 2.1.1.4.1 credit quality step 1 660 2.1.1.4.2 credit quality step 2 670 2.1.1.4.3 credit quality step 3 680 2.1.1.5 non financial corporate bonds 690 2.1.1.5.1 credit quality step 1 700 2.1.1.5.2 credit quality step 2 710 2.1.1.5.3 credit quality step 3 720 2.1.1.6 residential mortgage backed securities of credit quality step 1 730 2.1.1.7 other assets 740 2.1.1.8 of which central bank open market operations 750 2.1.2 Non-central bank eligible but tradable assets 760 2.1.2.1 equities listed on a recognised exchange, not self issued or issued by financial institutions 770 2.1.2.2 gold 780 2.1.2.3 other assets 790 2.1.3 of which from intragroup entities 800 2.2 Monies due not reported in 2.1 from customers that are not financial customers 810 2.2.1 from retail customers 820 2.2.2 from non-financial corporate customers 830 2.2.2.1 of which are intragroup entities

840 2.2.3 from central banks 850 2.2.4 from other entities 860 2.2.4.1 of which are intragroup entities 870 2.2.4.2 of which are public sectior entities 880 2.3 Monies due not reported in 2.1 from financial customers 890 2.3.1 from credit institutions 900 2.3.1.1 of which are intragroup entities 910 2.3.2 from financial customers other than credit institutions 920 2.3.2.1 of which are intragroup entities 930 2.3.3 of which are members of an institutional network 940 2.4 FX-swaps maturing 950 2.5 Amount receivable expected from the contracts listed in Annex II of CRR other than those reported in item 2.4 960 2.6 Paper in own portfolio maturing 970 2.7 Other cash inflows 980 2.7.1 of which from intragroup entities 990 2.8 Of which: Interest flows received 1000 2.8.1 of which from intragroup entities 1010 2.9 Total inflows 1020 2.10 Net funding gap 1030 2.11 Cumulated net funding gap

1040-1420 3 COUNTERBALANCING CAPACITY

1040 3.1 Cash 1050 3.2 Exposures to central banks 1060 3.3 Unencumbered Central Bank eligible collateral 1070 3.3.1 securities with a 0% risk weight 1080 3.3.1.1 representing claims on sovereigns 1090 3.3.1.2 guaranteed by sovereigns

1100 3.3.1.3 representing claims on or guaranteed by central banks

representing claims on or guaranteed by public sector entities, regions with fiscal autonomy to raise and collect taxes and local 1110 3.3.1.4 authorities

representing claims on or guaranteed by the Bank for International Settlements, the International Monetary Fund, the European Union 1120 3.3.1.5 or multilateral development banks 1130 3.3.1.6 representing claims on or guaranteed by the European Financial Stability Facility and the European Stability Mechanism 1140 3.3.2 securities with a 20% risk weight 1150 3.3.2.1 representing claims on sovereigns 1160 3.3.2.2 guaranteed by sovereigns 1170 3.3.2.3 representing claims on or guaranteed by central banks representing claims on or guaranteed by public sector entities, regions with fiscal autonomy to raise and collect taxes and local 1180 3.3.2.4 authorities 1190 3.3.2.5 representing claims on or guaranteed by multilateral development banks 1200 3.3.3 bonds eligible for the treatment set out in Article 129(4) or (5) of CRR 1210 3.3.3.1 credit quality step 1 1220 3.3.3.2 credit quality step 2 1230 3.3.3.3 credit quality step 3 1240 3.3.4 bonds as defined in Article 52(4) of Directive 2009/65/EC other than those referred to in item 3.3.3 1250 3.3.4.1 credit quality step 1 1260 3.3.4.2 credit quality step 2 1270 3.3.4.3 credit quality step 3 1280 3.3.5 non financial corporate bonds 1290 3.3.5.1 credit quality step 1 1300 3.3.5.2 credit quality step 2 1310 3.3.5.3 credit quality step 3 1320 3.3.6 residential mortgage backed securities of credit quality step 1 1330 3.3.7 other central bank eligible assets (including credit claims) 1340 3.4 Other unencumbered non central bank eligible, tradeable assets 1350 3.4.1 equities listed on a recognised exchange, not self issued or issued by financial institutions 1360 3.4.2 gold 1370 3.5 Undrawn committed credit lines granted to the reporting institution 1380 3.5.1 by members of the institutional network 1390 3.5.2 by intragroup entities 1400 3.5.3 by other entities 1410 3.6 Net change of Counterbalancing Capacity

1420 3.7 Cumulated Counterbalancing Capacity

Annex 2 – mapping of the maturity ladder used for stress tests

Correspondence with the Aggregate maturity ladder LT unsecured issuances maturing 020+030 Secured issuances maturing 040+050+060 ST paper due 070

120+130+140+180+220+260 Repos maturing +270+300+310+320 Retail deposits outflows 350 Corporate deposits outflows 360 OUTFLOWS Central Bank deposits outflows 380 Other deposits outflows 390 Financial deposits outflows 420 FX‐swaps outflows 490 Derivatives outflows 500 Other outflows 510

580+590+600+640+680+720+ Reverse repos 730+760+770+780 Retail inflows 810

Corporate inflows 820 Central Bank inflows 840 Other entities inflows 850

INFLOWS Fin. Inst. inflows 880 FX‐swap inflows 940 Derivative inflows 950 Other inflows 970

Cash 1040 Central Bank exposures 1050 0% RW securities 1070 CAPACITY 20% RW securities 1140 Covered bonds 1200 + 1240 Corporate bonds 1280 RMBS 1320 Other central bank eligible assets 1330 Non‐central bank eligible equities 1350 Other non‐central bank eligible assets 1340 ‐ 1350 COUNTERBALANCING Undrawn committed credit lines 1370

As regards funding sources, here are some examples of shocks observed on various funding sources.

Annex 3 ‐ Magnitude of Runs on Funding—Empirical Evidence and Stress Test Assumptions

(Source: IMF, Next generation of system‐wide liquidity stress testing)

Loss of Customer Deposits Loss of Wholesale Funding Empirical evidence Banking System in Saudi Arabia 11 Percent (1 week) (August 1990) Banesto (ES, 1994) 8 percent (1 week) Banking System in Argentina Deposits in domestic currency: (2001) 30 percent (9 months) Northern Rock (UK, 2007) 57 percent (12 months) 57 percent (6 months) Parex Bank (LV, 2008) 25 percent (3 months) IndyMac (US, June 2008) 7.5 percent (1 week) Washington Mutual (US, 8.5 percent (10 days) September 2008) DSB Bank (NL, 2009) 30 percent (12 days) Regulatory Parameters (unsecured categories) LCR (30 days) Stable: min. 5 Stable SME: min. 5 Less stable: min. 10 Less stable SME: min. 10 Non‐financial corporate, public sector: 75 All other deposits: 100 (secured) Repos: 0‐25 (quality collateral), 100 otherwise Regulatory Parameters Stable: 10 (unsecured categories) NSFR Less stable: 20 Short‐term corporate & public sector (< 1 year): 50 Rest: 100 Recent FSAPs 10‐50 percent (up to 80 percent 10 to 50 percent for non‐bank for non‐resident deposits) deposits 100 percent for bank funding 50 to 100 for parent funding

Annex 4 ‐ scenarios used by the IMF in its own set of stress tests

(Source: IMF, Next generation of system‐wide liquidity stress testing)

Annex 5: detailed results of the stress tests

Large universal bank

Baseline Idiosyncratic Combined Outflows Unsecured funding (ST & LT) ‐2.36% Secured funding 0.00% ‐0.09% Repos ‐7.99% ‐4.96% ‐7.99% Retail & corporate deposits Retail stable ‐0.04% ‐0.05% Retail unstable ‐0.10% ‐0.13% Corporate operational ‐0.12% ‐0.09% Corporate non‐operational ‐0.33% ‐0.28% Central bank Other deposits ‐0.09% ‐0.10% Interbank deposits ‐1.24% ‐2.37% Derivatives & contingent funding ‐20.47% ‐49.81% Committed facilities provided ‐1.13% Inflows Reverse repos 7.95% 5.66% 7.95% Retail & corporate 0.61% Central bank 2.00% 2.42% Other 0.51% Financial institutions 1.48% Derivatives 20.62% 49.76% Others Derivatives (adverse+ collateral posted) ‐3.88% 3 notch downgrade ‐0.68% Debt buy backs 0.00% CBC Cash 0.09% 0.09% 0.09% ECB eligible + 9.64% 8.43% 8.67% ECB eligible 0.17% 0.13% 0.14% Non‐ECB eligible 0.45% 0.25% 0.18%

Small diversified banks

Baseline Idiosyncratic Combined Outflows Unsecured funding (ST & LT) ‐1.03% Secured funding 0.00% ‐0.34% Repos ‐1.91% ‐1.63% ‐1.91% Retail & corporate deposits Retail stable ‐0.47% ‐0.29% Retail unstable ‐1.53% ‐0.96% Corporate operational ‐0.15% ‐0.11% Corporate non‐operational ‐0.82% ‐0.59% Central bank Other deposits ‐0.01% ‐0.08% Interbank deposits ‐1.17% ‐1.82% Derivatives & contingent funding ‐2.42% ‐7.27% Committed facilities provided ‐0.37% Inflows Reverse repos 3.10% 2.47% 3.10% Retail & corporate 0.61% Central bank 0.00% 0.00% Other 0.42% Financial institutions 1.14% Derivatives 2.42% 7.22% Others Derivatives (adverse+ collateral posted) ‐1.95% 3 notch downgrade ‐0.79% Debt buy backs 0.00% CBC Cash 0.31% 0.31% 0.31% ECB eligible + 6.23% 7.19% 5.60% ECB eligible 1.43% 1.58% 1.15% Non‐ECB eligible ‐0.94% ‐0.47% ‐0.38%

Asset management bank

Baseline Idiosyncratic Combined Outflows Unsecured funding (ST & LT) 0.00% Secured funding 0.00% 0.00% Repos ‐0.53% ‐0.53% ‐0.53% Retail & corporate deposits Retail stable 0.00% 0.00% Retail unstable ‐0.02% ‐0.02% Corporate operational 0.00% 0.00% Corporate non‐operational ‐0.03% ‐0.02% Central bank Other deposits ‐0.23% ‐0.47% Interbank deposits ‐16.06% ‐16.82% Derivatives & contingent funding ‐10.68% ‐59.30% Committed facilities provided ‐0.25% Inflows Reverse repos 11.28% 9.06% 11.28% Retail & corporate 0.09% Central bank 12.45% 12.45% Other 2.33% Financial institutions 10.51% Derivatives 10.68% 59.27% Others Derivatives (adverse+ collateral posted) ‐0.99% 3 notch downgrade 0.00% Debt buy backs 0.00% CBC Cash 0.00% 0.00% 0.00% ECB eligible + 6.38% 6.36% 5.74% ECB eligible 0.62% 0.72% 0.50% Non‐ECB eligible 0.00% 0.00% 0.00%

Bibliography

Papers issued by regulators  ACPR, Analyses et synthèses, Stress tests sur le système bancaire et les organismes d’assurance en France, N°11, January 2013  BCBS, working paper N°24, Liquidity stress testing, a survey of theory, empirics and current industry and supervisory practices, October 2013  BCBS, working paper N°25, Literature review of factors relating to stress test – extended version, October 2013  BCBS, working paper N°238, Basel III, the liquidity coverage ratio and liquidity risk monitoring tools, January 2013  BCBS, working paper N°295, Basel III, the net stable funding ratio, October 2014  BCBS, working paper N°316, Funding liquidity risk, definition and measurement, Mathias Drehmann, Kleopatra Nikolaou, July 2010  Towards a framework for quantifying systemic stability, Piergiorgio Alessandri (Bank of England), Prasanna Gai (Australian National University), Sujit Kapadia (Bank of England), Nada Mora (Bank of England), and Claus Puhr (Oesterreichische Nationalbank)  Czech National Bank, working paper series 11, Models for Stress Testing Czech Banks´ Liquidity Risk, Zlatuše Komárková, Adam Geršl, Luboš Komárek, November 2011  ECB, working paper series N°1024, Funding liquidity risk, definition and measurement, Mathias Drehmann, Kleopatra Nikolaou, March 2009  Bank of England, Financial stability paper N°11, Intraday liquidity, risk and regulation, Alan Ball, Edward Denbee, Mark Manning and Anne Wetherilt, June 2011  Bank of England, Working paper N°372, Funding liquidity risk in a quantitative model of systemic stability, David Aikman, Piergiorgio Alessandri, Bruno Eklund, Prasanna Gai, Sujit Kapadia, Elizabeth Martin, Nada Mora, Gabriel Sterne, Matthew Willison, June 2009  CEBS, Guidelines on liquidity buffers and survival periods, December 2009  DNB working paper, N°175, Liquidity stress tester, a macro model for stress testing banks’ liquidity risk, Jan Willem van den End, May 2008  IMF working paper, Next generation of system‐wide liquidity stress testing, Christian Schmieder, Heiko Hesse, Benjamin Neudorfer, Claus Puhr, Stefan W. Schmitz, January 2012  IMF working paper, Measuring Systemic Risk‐Adjusted Liquidity (SRL) ‐ A Model Approach, Andreas A. Jobst, August 2012

Various articles  The arbitrage‐free valuation and hedging of demand deposits and credit card loans, Robert A. Jarrow, Donald R. van Deventer, Journal of Banking & Finance, 1998  How Should We Hedge Deposit Accounts?, A. Adam, J‐P. Laurent & C. Rebérioux, September 2004  Measuring Bank Funding Liquidity Risk, Fidelis T Musakwa, April 2013  Bank liquidity management and supervision, which lessons from recent market turmoil?, Gianfranco A. Vento, Pasquale la Ganga, Journal of investment, money and banking, 2009

 Modeling Liquidity Risk, With Implications for Traditional Market Risk Measurement and Management, Bangia, A., Diebold, F.X., Schuermann, T, and Stroughair, J. (2001), in S. Figlewski and R. Levich (eds.), Risk Management: The State of the Art . Amsterdam: Kluwer Academic Publishers, 2002, 1‐13  An implied prepayment model for MBS, Eknath Belbase, PhD, Quantitative perspectives, January 2001  Dynamic modelling and optimization of non‐maturing accounts, Karl Frauendorfer Michael Schürle, Institute for Operations Research and Computational Finance, University of St. Gallen, Switzerland  Bank of Canada, Understanding and measuring liquidity risk: A Selection of Recent Research, Céline Gauthier, Financial Stability Department and Hajime Tomura, Funds Management and Banking, 2011  Risk management of non‐maturing liabilities, Michael Kalkbrenner, Jan Willing  Recent Advances in Modeling Liquidity Risk and Applications to Central Clearing , Marco Avellaneda, New York University and Finance Concepts LLC, Global Derivatives USA, November 20, 2013  Introducing Funding Liquidity Risk in a Macro Stress‐Testing Framework, Céline Gauthier (Bank of Canada), Moez Souissi (International Monetary Fund), Xuezhi Liu (Manulife Financial)  Modelling and Managing Liquidity Risk, Gary G. Venter, Society of Actuaries, Schaumburg, Illinois, 2010  Theory and Practice of Timeline Simulation, Rodney Kreps, Casualty actuarial society  Liquidity Cash Flow Planning and Stress Testing Model, User’s Guide, Young & associates  Liquidity Risk: What is it? How to Measure it? René Garcia, EDHEC Business School, Cirano, Montreal, January 7, 2009  Office of financial research, brief series, Incorporating Liquidity Shocks and Feedbacks in Bank Stress Tests, Jill Cetina, 2015  The arbitrage‐free valuation and hedging of demand deposits and credit card loans, Jarrow, R. and van Deventer, D. (1998), Journal of Banking & Finance, 22, 249‐272

Books

 Liquidity Risk Management in Banks: Economic and Regulatory Issues, Ruozi, Roberto, Ferrari, Pierpaolo. 2012.  Managing Liquidity in Banks: A Top Down Approach Duttweiler, Rudolf. 2009.  Liquidity modelling, Robert Fiedler. 2011.  Liquidity Risk Management in Banks: Economic and Regulatory Issues, Ruozi, Roberto, Ferrari, Pierpaolo, 2013  Bank Asset‐Liability and Liquidity Risk Management Choudhry, Moorad, Landuyt, Gino 2011  Capital, Contingent Capital, and Liquidity Requirements Acharya, Viral V. ; Cooley, Thomas F. ; Richardson, Matthew ; Walter, Ingo 2011  Risk and liquidity Hyun Song, Shin 2010.  Liquidity regulation, funding costs and corporate lending Bonner, Clemens 2012

 Liquidity risk: managing asset and funding risk, Erik Banks. Banks, Erik 2005.  Liquidity risk: managing funding and asset risk, Erik Banks. Banks, Erik 2014.  Bank liquidity, the maturity ladder, and regulation Haan, Leo De End, Jan ‐ Willem Van Den 2012  Modelling the liquidity ratio as macroprudential instrument Willem, Jan Kruidhof, Mark 2012  Handbook of asset and liability management: from models to optimal return strategies Adam, Alexandre. 2007.  Handbook of asset and liability management, Zenios, Stavros Andrea. ; Ziemba, 2006  Asset and liability management tools : a handbook for best practice Bernd Scherer.  Asset‐liability gap Moles, P. ; Terry, N. 1997  Liquidity Risk Management, Matz, Leonard M. 2001.  Funding liquidity risk: definition and measurement, Drehmann, Matthias. ; Nikolaou, Kleopatra. European Central Bank. (Editor) 2009.  Funding liquidity risk : definition and measurement, Drehmann, Mathias Nikolaou, Kleopatra 2009  The Net Stable Funding Ratio, Gobat, Jeanne. Yanase, Mamoru. Maloney, Joseph. 2014.  Stress testing and contingency funding plans: an analysis of current practices in the Luxembourg banking sector, Franco Stragiotti. Stragiotti, Franco. Banque centrale du Luxembourg. (Editor) 2009.