Managing Settlement Risk in Banking Þórdís Sara Ársælsdóttir

Managing Settlement Risk in Banking

Þórdís Sara Ársælsdóttir

Thesis of 30 ECTS credits Master of Science (M.Sc.) in Management Engineering

June 2018

Managing Settlement Risk in Banking

Thesis of 30 ECTS credits submitted to the School of Science and Engineering at Reykjavík University in partial fulfillment of the requirements for the degree of Master of Science (M.Sc.) in Management Engineering

June 2018

Supervisor: Sverrir Ólafsson, Supervisor. Professor, School of Science and Engineering Reykjavík University, Iceland

Examiner: Yngvi Harðarson, Examiner MA in Economics, Director of Analytica.

Managing Settlement Risk in Banking

Þórdís Sara Ársælsdóttir

June 2018

Abstract Settlement risk has recently become a hot topic in the risk management of financial institutions. Scandinavian banks have started to consider it in their Pillar 3 Reports and capital requirements. Settlement risk is the risk that a counterparty fails to fulfil its end of a contract of delivering securities or their value in cash, when the security/cash has already been delivered.

A lot of the research and publications on settlement risk focus on the systematic approach of mitigating settlement risk. In this thesis the focus is on identifying and quantifying settlement risk by using financial mathematical methods. The thesis works with retrieved data to detect which instruments contain the most risk. The focus is on settlement time as well as a search for patterns on exposure versus the risk taken.

The fundamental mathematical techniques applied are based on the assumption that prices follow a geometric Brownian motion process. We then apply Ito’s Lemma, arbitrage techniques and basic probabilistic methods to quantify the settlement risk exposure.

viii

Stýring Uppgjörsáhættu í Bankastarfssemi

Þórdís Sara Ársælsdóttir

júní 2018

Útdráttur Uppgjörsáhætta hefur nýlega orðið vinsælt umræðuefni í áhættustýringu fjármálafyrirtækja. Skandinavísku bankarnir hafa byrjað að gera grein fyrir henni í áhættuskýrslum sínum og eiginfjárþörf. Uppgjörsáhætta er áhættan, fólgin í því að mótaðili uppfylli ekki samninginn að afhenda verðbréf eða virði þeirra í peningum, þegar að verðbréfið eða virði þeirra í peningum hefur þegar verið afhent.

Margar af þeim birtu rannsóknum um uppgjörsáhættu snúast um kerfislegar aðferðir við mildun uppgjörsáhættu. Í þessari ritgerð verður áherslan lögð á að meta uppgjörsáhættu með því að notast við aðferðir fjármálastærðfræðinnar.

Verkefnið snýst um að greina hvaða fjármálagjörningar í ákveðnum banka innihalda uppgjörsáhættu, sækja viðeigandi gögn fyrir þá fjármálagjörninga, mæla áhættuna og koma með aðferðir til að milda áhættuna. Grundvallar stærðfræðilegu aðferðirnar notaðar byggjast á þeirri forsendu að verðin fylgja Geometric Brownian Motion ferli. Því næst beitum við Ito’s Lemma, ásamt öðrum aðferðum fjármálastærðfræðinnar til að magnsetja uppgjörsáhættu.

Managing Settlement Risk in Banking

Þórdís Sara Ársælsdóttir

June 2018

Student:

Þórdís Sara Ársælsdóttir

Supervisors:

Sverrir Ólafsson

Examiner:

Yngvi Harðarson

xii

The undersigned hereby grants permission to the Reykjavík University Library to reproduce single copies of this Thesis entitled Managing Settlement Risk in Banking and to lend or sell such copies for private, scholarly or scientific research purposes only.

The author reserves all other publication and other rights in association with the copyright in the Thesis, and except as herein before provided, neither the Thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author’s prior written permission.

date

Þórdís Sara Ársælsdóttir Master of Science

xiv

Acknowledgements

To my supervisor at Reykjavik Unversity, Sverrir Ólafsson, for believing in the topic as well as his support and suggestions on the thesis.

To my partner, Halla Marinósdóttir for always believing in me and showing me patience.

To my supervisor at the bank for his input, support and weekly meetings. To everyone at the bank, especially IT, for all your help.

vii

Contents

List of Figures ix

List of Tables xi

1 Introduction 1 1.1 Research Scope and Objective ...... 1 1.2 Outline of Thesis ...... 2

2 Risks Financial Institution’s Face 3 2.1 Settlement Risk ...... 5 2.1.1 Foreign Exchange ...... 5 2.1.2 Ways of Mitigating FX Settlement Risk ...... 7 2.2 Why Should Banks Have an Interest in Settlement Risk ...... 9 2.3 What have the Scandinavian Banks Been Doing? ...... 10 2.3.1 Jyske Bank ...... 11 2.3.2 Nordea ...... 11 2.3.3 SEB ...... 11 2.3.4 Handelsbanken ...... 12 2.3.5 Swedbank ...... 12 2.3.6 Deutsche Bank ...... 13 2.4 Settlement Time ...... 13

3 Settlement Risk at the Bank 15 3.1 Example of Exposure to Settlement Risk at the Bank ...... 16 3.2 Stocks ...... 16 3.2.1 Domestic Market ...... 16 3.2.2 International Market ...... 18 3.3 Funds ...... 20 3.4 Derivatives ...... 21 viii

3.4.1 Forward Contracts ...... 22 3.4.2 Options ...... 25 3.4.3 Swaps ...... 28 3.5 Foreign Exchange ...... 29

4 Methods 31 4.1 Data ...... 31 4.1.1 Stocks ...... 31 4.1.2 Derivatives ...... 32 4.1.3 Foreign Exchange ...... 34 4.1.4 Historical Data on Shares and Funds ...... 34 4.1.5 Historical Data for Offered Interbank Rate Depending on Currency 36 4.2 Geometric Brownian Motion ...... 37 4.3 Maximum-Likelihood Estimation Method ...... 38 4.4 Probability of FX Rate Being Smaller than Some Value K Using Geomet- ric Brownian Motion ...... 40

5 Results 41 5.1 Statistics ...... 41 5.1.1 Stocks ...... 41 5.1.2 Derivatives ...... 44 5.1.3 Foreign Exchange ...... 47 5.2 Fitting the Parameters ...... 49 5.2.1 Shares ...... 50 5.2.2 Funds ...... 51 5.2.3 FX Rates ...... 52 5.3 Probability that the Stock Price at Time T is Less than at Time t Plus Fees 53 5.3.1 Stocks ...... 53 5.3.2 Equity Forwards ...... 59 5.4 Probability of the Exchange Rate of a Currency Cross at Time T Being Less than at Time t Plus Cost ...... 64

6 Conclusion 67 6.1 Recommendations for the Bank ...... 67 6.2 Limitations ...... 68 6.3 Further Work ...... 68

Bibliography 71 ix

List of Figures

2.1 Counter party risk deﬁned and where settlement risk ﬁts in ...... 4 2.2 An example of foreign exchange between two banks, A and B, where they’re trading JPY and USD respectively ...... 6 2.3 An example of how CLS works as an intermediate to settle a foreign exchange trade between two Banks ...... 9

3.1 The process of trading shares and where exposure to settlement risk arises, domestic market...... 17 3.2 The process of trading shares and where exposure to settlement risk arises, international market...... 19 3.3 The process of delivery of funds and where exposure to settlement risk arises, domestic market...... 21 3.4 European options and payoffs depending on if it is a) long call, b) short call, c) long put or d) short put. Image from Options, Futures and Other Derivatives by John C. Hull...... 26 3.5 How settlement risk can occur when Íslandsbanki is in a forward swap contract with a counterparty ...... 29

4.1 How stock trades can either go through or not at after the bank has purchased the stock, thus leading to settlement risk ...... 32

5.1 A histogram of the amounts traded on a log-10 scale for every stock type (with 80 bins)...... 42 5.2 Total amount traded with the settlement time ranging from 0-21 days. . . 42 5.3 A histogram of the amounts traded on a log-10 scale for every stock type (with 80 bins)...... 43 5.4 A histogram of reversed trades on a log-10 scale for every stock type (with 50 bins)...... 44 x

5.5 Equity and bond forwards where the net amount paid either by the bank (negative) or counterparty (positive) is on y-axis. X-axis represents days before/after maturity date where the forwards are completed...... 45 5.6 Histogram of the log10 value of net amounts of forwards where the counterparty owes the bank at maturity date...... 46 5.7 The net amount counterparties owe the bank on y-axis and day before/after maturity date on x-axis...... 47 5.8 Histogram of the probability of S(T ) S(t)(1 + c ) for Icelandic shares,  r where the trade count is represented on the y-axis and the probability on the x-axis...... 54 5.9 Log10 value of amounts of reversed trades filtered on Icelandic stock type. 55 5.10 Histogram of the probability of S(T ) S(t)(1 + c ) for foreign shares,  r where the trade count is represented on the y-axis and the probability on the x-axis...... 56 5.11 Log10 value of amounts of reversed trades filtered on foreign stock type. . 56 5.12 Histogram of the probability of S(T ) S(t)(1 + c ) for Icelandic shares,  r where the trade count is represented on the y-axis and the probability on the x-axis...... 57 5.13 Log10 value of amounts of reversed trades filtered on Icelandic fund type. 58 5.14 Histogram of the probability of S(T ) S(t)(1 + c ) for foreign funds,  r where the trade count is represented on the y-axis and the probability on the x-axis ...... 59 5.15 Log10 value of amounts of reversed trades filtered on foreign fund type. . 59 5.16 A tree explaining the scenarios in equity forwards the bank can be in and when it’s better if the probability of S(T ) S(t)(1 + c ) are high or low. 61  r 5.17 The ratio between the bank’s two positions of being the buyer or seller. . . 62 5.18 The probability that S(T ) S(t)(1 + c ) for equity forwards where the  r bank holds the buyer position...... 62 5.19 The probability that S(T ) S(t)(1 + c ) for equity forwards where the  r bank holds the seller position...... 63 5.20 A histogram of the probability of X(T ) X(t)(1 + c ) for foreign ex-  r change forwards and the underlying currency crosses...... 65 xi

List of Tables

2.1 Minimum capital requirement and risk exposure amount due to settlement risk for years 2014 and 2015 ...... 12

3.1 Four alternatives of pay and delivery in forward contracts...... 22 3.2 Payoff depending on position in European call and put otpions...... 26

4.1 The shares, for which data was retrieved from Kauphöllin and Yahoo Fi- nance for the year 2017 with 250 business days...... 35 4.2 The funds, for which data was retrieved from various sources for the year 2017 with 250 business days...... 36 4.3 Interest rates retrieved for each currency...... 37

5.1 Average time (in days) it takes to settle equity and bond forwards, thus settlement time (T + x) from maturity date (T ) ...... 45 5.2 The five instances where the Bank was exposed to settlement risk for 1-5 minutes in FX forwards...... 49 5.3 The fitted parameters µˆ and ˆ for Icelandic and foreign stocks on market. 50 5.4 The fitted parameters µˆ and ˆ for the funds the bank trades for customers. 51 5.5 Annualized volatility for the foreign exchange rates X(t) (maximum likelihood estimation method, year 2016)...... 52 5.6 The Icelandic stocks divided into five risk categories...... 63 5.7 An example of how an increase/decrease in the exchange rate X(T ) in FX forward contracts affects the bank...... 64 5.8 The underlying currency crosses in FX forwards divided into five risk categories...... 66 xii 1

Chapter 1

Introduction

Credit risk is a term most people are familiar with. Credit risk methods have been in de- velopment for about 30 years (E. I. Altman, 1998). Credit risk can be further broken down into counterparty and issuer risk. Issuer risk is the more common one, at least for corporate banks, and is the risk that a borrower will default on its obligations. Counterparty risk is the term used for trading partners, unlike issuer risk, which refers to borrowers, and has three types of risks depending on the type of deal. The three distinct types of counterparty risks are: default risk, replacement risk and settlement risk (Borio et al., 2008).

Settlement risk has quickly become a hot topic in the risk management of ﬁnancial institutions. The Scandinavian banks have started to consider it in their Pillar 3 Reports and capital requirements. Settlement risk is the risk that a counterparty fails to fulﬁll its end of a contract of delivering securities or its value in cash when the security/cash has already been delivered (Borio et al., 2008).

The content, settlement risk, was a little bit difficult to work with in the beginning of the project. A lot of the research and publications on settlement risk focus on the systematic approach of mitigating settlement risk. In this thesis the focus is on identifying and quantifying settlement risk by using financial mathematical methods. The content of this report is therefore state of the art in its field.

1.1 Research Scope and Objective

The project is to deﬁne which ﬁnancial instruments at a certain bank contain settlement risk. The thesis works with retrieved data to detect which instruments contain the most 2 Managing Settlement Risk in Banking risk. The focus is on settlement time as well as a search for patterns on exposure versus the risk taken.

1.2 Outline of Thesis

The remainder of this thesis is organized as follows. Chapter two provides a brief overview of risk management at financial institutions and where settlement risk fits in. The attempt to cover the background of settlement risk is in chapter two as well. As stated in the introduction it was difficult to find available material on settlement risk. Thus much focus is on settlement risk in foreign exchange transactions between two banks. The chapter also provides an overview of how the Scandinavian banks have covered settlement risk in their Pillar 3 reports. The aim of chapter three is to grasp in words and images how and if the bank is exposed to settlement risk in the different instruments. Chapter three is based on multiple interviews with the bank’s employees as well as the bank’s quality manual and work instructions. Chapter four describes the data that needed to be retrieved and from where. Chapter four also explains the methods used to estimate the probabilities of loss for the bank if exposed to settlement risk. Chapter five presents the results of the thesis. The chapter begins by providing a statistical overview of settlement risk at the bank, in which financial instruments the bank is exposed, exposure amounts and so on. The chapter ends on providing the probability of loss for the bank if exposed to settlement risk in the different contracts. The final chapter, chapter 6, provides the final conclusions. Thus the recommendations for the bank, limitations and possible further work. 3

Chapter 2

Risks Financial Institution’s Face

The motivation for ﬁnancial institutions for managing and modelling credit risk stems from the need to quantify the amount of capital needed to support a bank’s exposure. Credit risk models take the state of the economy and of the ﬁrm under consideration as inputs and gives the credit spread as an output. (Chatterjee, 2015).

A common way of dividing the risk management at ﬁnancial institutions is: (Íslandsbanki, 2016)

Credit Risk • Market Risk • Liquidity Risk • Operational Risk •

Credit risk can be further broken down into counterparty and issuer risk (ﬁgure 2.1). Issuer risk is the more common one, at least for corporate banks, and is the risk that a borrower will default on its obligations. Counterparty risk is the term used for trading partners, unlike issuer risk, which refers to borrowers, and has three types of risks depending on the type of deal. The three distinct types of counterparty risk are: default risk, replacement risk and settlement risk. (Beier, Harreis, Poppensieker, Sojka, & Thaten, 2010) 4 Managing Settlement Risk in Banking

Figure 2.1: Counter party risk deﬁned and where settlement risk ﬁts in

Credit risk is defined as the risk to earnings and capital if an obligor would fail to meet its obligations to a contract with a financial institution. Credit concentration is also commonly measured and is defined as the increase in risk driven by underlying factors such as geographical location, type of financial instrument, sector or due to connections or relations among counterparties. Market risk differs from credit risk in that it’s not a risk directly driven by obligors. Market risk is the current or potential risk to earnings and capital due to movements in the volatility of prices of market instruments, such as changes in interest rates, equity prices and foreign exchange rates. Liquidity risk is defined as the risk of not being able to fund financial obligations or planned growth, or only being able to do so substantially above the prevailing market cost of funds. At last, operational risk is defined as the risk of loss resulting from inadequate or failed internal processes, systems, people or from external events (Íslandsbanki, 2016). Þórdís Sara Ársælsdóttir 5

2.1 Settlement Risk

The fundamental deﬁnition of settlement risk is that it’s the risk that one counter party fails to fulﬁll it’s end of the agreement of delivering the securities or it’s value in cash when the security has been traded and the other counterparty has delivered the cash value of the security as was agreed upon. (Borio et al., 2008)

Although a substantial progress has been made in mitigating settlement risk, especially for foreign exchange transactions. A survey conducted by the Committe on Payment and Settlement Systems (CPSS), revealed that ﬁnancial institutions still have some work to do. Banks, industry groups and central banks should therefore have an increased interest in managing and mitigating settlement risk. The growth of the FX market since 2000 has resulted in that the amount settled via non-PVP1 methods might not be less than before PVP2 methods existed.

2.1.1 Foreign Exchange

One type of trade where exposure to settlement risk can occur is when foreign exchange transactions take place also known as the Herstatt risk.3 FX settlement risk arises when there is no mechanism to ensure payment-versus-payment (PVP), where you only pay when you get paid. Both counter parties then expose themselves to settlement risk which can take place for often more than a day. FX settlement risk entails

Principal Risk • Replacement Cost Risk • Liquidity Risk • Operational Risk • Legal Risk • which have been mitigated by implementation of payment-versus-payment arrangements, increased use of close-out netting and collateralisation. Before the different types of foreign exchange related risks are explained in more details, an example of how foreign exchange transactions work and how settlement risk can arise

1 non-payment-versus-payment 2 Payment-versus-payment 3 Referring to the German bank which was closed by German authorities in 1974 midst trading a security where their counter party had already paid them Deutsche marks.(Borio et al., 2008) 6 Managing Settlement Risk in Banking will be taken. (Bank for International Settlements, 2013)

Example: Bank A is having a spot trade4 with bank B. Bank A is selling yen in exchange for US dollars from bank B. The trade is executed on day T-2 where T is the settlement date or value day. Figure 2.2 displays how bank A instructs its correspondent in Japan (Ja) to send yens to bank B’s correspondent in Japan (Jb) on settlement day (V). Bank Ja fulﬁlls bank A’s request sometimes during day V by debiting the account bank A has and sends the yen to bank Jb via the payment system. Bank Jb credits the funds to bank B after receiving the funds from bank Ja. Bank B settles its side of the trade by instructing its correspondent in the US (Ub) to send US dollars to Bank A’s correspondent in the US.

Figure 2.2: An example of foreign exchange between two banks, A and B, where they’re trading JPY and USD respectively

Settlement risk in this example is due to the fact that either bank A or bank B might pay the currency they are selling but not receive the one they are purchasing. A simultaneous link of the trading between the counter parties is missing. The exposure to settlement risk bank A faces starts when it can no longer cancel its instructions to transfer the yen to bank B. The exposure for bank A ends when bank Ua has credited the funds to bank A. (Borio et al., 2008).

Principal risk refers to the risk of losing the full value of a trade resulting of a counter party defaulting, e.g. Herstatt Risk. It’s the most serious of the risks because the amount at risk can be equal to the full value of the trade. Around the year 2000 more concern

4 Spot trade is where the purchase or sale of a foreign currency e.g., is meant for immediate delivery. Þórdís Sara Ársælsdóttir 7 went into mitigating principal risk and banks are now encouraged to use FMIs that offer PVP settlement when settling FX transactions.(Bank for International Settlements, 2013)

It is recommended by BCBS5 to mitigate replacement cost risk by using netting arrangements where applicable and collateral arrangements. Replacement cost risk is the risk which occurs when a counterparty defaults before settlement day forcing the bank to replace the old existing trade with a new trade and counter party at current market prices, which could be less favorable for the bank. The bank might therefore encounter a loss relative to the difference of the exchange rate. (Bank for International Settlements, 2013).

Liquidity Risk accounts for the risk that a counter party will not settle the full value of the debt when it is due. The counter party is not insolvent since it might settle the required debt obligations later on. Whether a default and the replacement cost risk becomes liquidity risk depends on if a bank is able to replace the failed trade to meet its obligations or borrow the currency needed until the bank can replace the trade. The probability of a trade resulting in liquidity shortage depends on three factors which are the timing of the default, if the bank has irrevocably paid away the currency it is selling and the nature of the trade. Also if a bank is able to make other arrangements when the default is closer to settlement date. The second factor is explained as follows, the bank might have fewer liquid assets to pay for the replacement trade or use as collateral for borrowing. The nature of the trade means that its harder to replace the trade if the currency being purchased is less liquid and/or if the value of the trade is larger. (Bank for International Settlements, 2013).

2.1.2 Ways of Mitigating FX Settlement Risk

There are ways of mitigating the foreign exchange settlement risk which are being exercised in most Scandinavian banks6. Some of those arrangements are close-out netting, collateral arraengements, payment-versus-payment and central clearing.(Bank for Inter- national Settlements, 2013).

Close-out netting arrangements are establishments where two counter parties agree upon a bilateral agreement which states that if a default occurs (insolvency of one counter party) the unpaid obligations which are covered by the netting agreement are netted. Close- out payments are concluded based on the net present value of future cash ﬂows between

5 Basel Committee on Banking Supervision 6 Jyske Bank, Nordea, SEB, Danske Bank and many more 8 Managing Settlement Risk in Banking a bank and the defaulting counter party. The value of multiple future cash ﬂows in a commitment are calculated to a net present value in one currency due to the closed-out counter party. Where close-out netting is legally enforceable it reduces principal risk, replacement cost risk, liquidity risk and operational risk for unsettled future commitments. Banks might be required to pay the principal to a defaulted counter party where close-out netting agreements have not been made. So the agreement ensures it won’t happen in jurisdictions where statutory provision is weak, not existent or ineffective.(Bank for In- ternational Settlements, 2013).

Replacement cost risk can be reduced even further if collateral arrangements accompany the netting. Collateral arrangement involves that the counter party with negative net position provides ﬁnancial assets as collateral to secure obligation.(Bank for International Settlements, 2013).

Principal risk can be removed by using the payment-versus-payment mechanism. That type of system involves, as the name suggests, that the final transfer of a payment in one currency happens only and only if a final transfer of payment in another currency occurs. The CLS Bank International currently offers this type of settlement arrangement. An- other type of PVP arrangement is where a link exists between two systems which offers a simultaneous payment between systems. Liquidity risk cannot be totally mitigated since PVP does not guarantee settlement, leaving a counter party short of the currency it tried to purchase.(Bank for International Settlements, 2013). An example of how CLS works can be seen in figure 2.3. CLS Bank settles FX trades in 17 currencies in North America, Africa, the Middle East and Europe. CLS uses the PVP methodology which is that you only get paid if you pay. On settlement date each bank pays the correspondent currency, but unlike before, CLS only pays the bought currency if the sold currency has been received. The trade still remains between the two counter parties but CLS is a trusted third party that enables elimination of principal risk.

Central clearing is another way of mitigating FX settlement risk where a central counter party poses itself between two counter parties trading and becomes the buyer of every seller and the seller to every buyer. (Bank for International Settlements, 2013). Þórdís Sara Ársælsdóttir 9

Figure 2.3: An example of how CLS works as an intermediate to settle a foreign exchange trade between two Banks

2.2 Why Should Banks Have an Interest in Settlement Risk

The Basel Committee on Banking Supervision (BCBS) argues that substantial FX settlement- related risk still remains due to growth in FX trading activities. Hence many banks are underestimating their principal risk and other risks associated with settlement risk. Such risks might not have a big impact under normal market condition, however under market stress they might create larger concerns. So BCBS is encouraging banks to manage FX settlement-related risks. Thus identify where the risks are, measure, monitor and control them. (Bank for International Settlements, 2013).

McKinsey published a report in 20107 where they put counterparty risk in the same league as market and liquidity risk after the great depression in 2008. They encourage banks to take matters in their own hands instead of waiting for new regulations. They also don’t count on new regulations to be a remedy and advocate four starting measures for banks:

Establish an accurate and timely way to measure counterparty risk • Improve the process by which they set risk limits and adhere to them • Leverage the full potential of netting agreements and collateral management • Improve management of counterparty risk in settlement and clearing • 7 (Beier et al., 2010) 10 Managing Settlement Risk in Banking

Authorities are calling for increased capital requirements. So by having a systematic approach to handling the risk, banks will not only mitigate unwanted risk, but also improve capital efﬁciency.

2.3 What have the Scandinavian Banks Been Doing?

The Scandinavian Banks publish a so called Pillar 3 report on a yearly basis. As stated in Íslandsbanki’s pillar 3 report its purpose is to:

"Pillar 3 Report is to provide market participants and other stakeholders with information that facilitates a better understanding of the Bank’s risk proﬁle and capital adequacy, in accordance with the Basel pillar 3 disclosure requirements. The Pillar 3 Report provides key information on Íslandsbanki’s risk governance, risk assessment processes, material risk exposures, capital adequacy and liquidity adequacy."8

If the Banks are considering settlement risk and ways of mitigating the risk it is most likely stated in their pillar 3 report. The Scandinavian Banks which will be looked into and their governance of settlement risk are:

Jyske Bank • Nordea • SEB • Handelsbanken • Swedbank • Danske Bank • Deutsche Bank • However Danske Bank does not discuss settlement risk in their risk management pillar 3 report, thus they will be discarded in this report.

8 https://www.islandsbanki.is/library/Skrar/IR/Afkoma/Pillar3Report2016.pdf Þórdís Sara Ársælsdóttir 11

2.3.1 Jyske Bank

Jyske Bank has a policy for managing counter party credit risk9 in where it distinguishes between small and larger counterparties. The way Jyske Bank measures the risk for these two types of counter parties is identical, however the management of the risk differenti- ates. They explicitly state in the report that they calculate settlement risk to manage and monitor large counter party exposures although they don’t say how. Jyske Bank reduces settlement risk by using CLS, when possible, where they are a third party member. The trades through CLS are payment-versus-payment based, thus reducing the settlement risk in FX transactions. For transactions involving derivatives Jyske Bank attempts to mitigate risk by clearing through a central counter party (CCP), requiring master netting agreements and attaching collateral management agreements to the master agreements. (Jyske Bank, 2016)

2.3.2 Nordea

Nordea states in their pillar 3 report that credit risk includes counterparty risk, transfer risk and settlement risk. Nordea deﬁnes settlement risk as the risk that arises during the process of settling a contract or executing a payment. Settlement risk is restricted by certain settlement risk limits for each counterparty. Coun- terparties are assessed in a credit process leading to clearing agents, corespondent banks and custodians being chosen in a way to minimize settlement risk. Nordea also eliminates FX settlement risk by the use of CLS with counterparties eligible for CLS clearing. They have a policy in place for non-eligible counterparties which is to settle via in-house accounts. For external settlements an approval is needed from a credit committee and in those cases Nordea uses bilateral payment netting to reduce principal amount. The risk exposure due to settlement risk was 1 EURm at year end of 2015 and zero on September 30th and December 31st in 2016. Minimum capital requirements due to settlement risk in 2016 was zero. (Nordea, 2016)

2.3.3 SEB

Skandinaviska Enskilda Banken (SEB) includes settlement risk, counter party risk derived from trading operations and country risk in their deﬁnition of credit risk.

9 The risk of loss due to a counterparty failing to fulﬁll its obligations (Jyske Bank, 2016) 12 Managing Settlement Risk in Banking

In their 2016 pillar 3 report they state that limits are established for settlement risk in trading operations. Settlement risk for FX transactions is monitored and the exposure is equal to the the FX settlement amount. When deciding on counter party limits, FX settlement risk is taken into account for those ﬁnancial instruments that include the risk. Limits are in place for all counterparties in trading instruments including FX settlement risk. SEB eliminates FX settlement risk when possible with counterparties that are eligible for CLS clearing. The risk exposure due to settlement risk was 1 SEKm at year end of 2015 and zero at year end of 2016. Minimum capital requirements due to settlement risk in 2016 was zero. (SEB, 2016)

2.3.4 Handelsbanken

Handelsbanken does not mention settlement risk in a text in the 2016 pillar 3 report. However, settlement risk is included in two tables. Both tables showing capital requirements and total risk exposures where settlement risk has no exposure. (Handelsbanken, 2016)

2.3.5 Swedbank

Swedbank approaches FX settlement risk in the same way as SEB, that is when deciding on counter party limits, FX settlement risk is taken into account for those ﬁnancial instruments that include the risk. Limits are in place for all counterparties trading instruments including FX settlement risk. Swedbank uses delivery-vs-payment (DVP) or payment-vs-payment (PVP) arrangements to mitigate settlement risk when possible. Swedbank eliminates FX settlement risk when possible with counterparties that are eligible for CLS clearing. The minimum capital requirement due to settlement risk was 2 SEKm in 2014 and 1 SEKm in 2015 and the risk exposure amount due to settlement risk was 30 and 7 SEKm respectively (ﬁgure 2.1). (Swedbank, 2015).

2015 2014 Minimum capital requirement for settlement risks 1 2 Risk exposure amount settlement risks 7 30 Table 2.1: Minimum capital requirement and risk exposure amount due to settlement risk for years 2014 and 2015 Þórdís Sara Ársælsdóttir 13

2.3.6 Deutsche Bank

Deutsche Bank calculates economic capital needed in a model that contains four risk modules. These risk modules are market risk, operational risk, business risk and credit risk which covers counter party (default) risk, transfer risk and settlement risk. Risk weighted assets by model approach and business division according to transition rules includes settlement risk exposure of 36 EURm on 31st of December 2016 and 9 EURm in 2015. Capital requirements due to settlement risk was 3 and 1 EURm in 2016 and 2015 respectively. Even though Deutsche Bank includes settlement risk in their model they don’t state in their report how they deﬁne, calculate or mitigate settlement risk. (Deutche Bank, 2016)

2.4 Settlement Time

Abbreviations such as T+2, T+3, T+14 will appear in this report with good reason. Trans- action date and settlement date are two terms that are closely related. T+2 stands for a settlement date which includes the transaction day (T) plus two business days (+2). So for example if you buy 100 shares in a stock on a Monday (in a week with no holidays) with the time T+2, Monday is the transaction date. The settlement date however is a Wednes- day and represents the date at which ownership is transferred. The settlement date varies depending on the type of security being traded, which can be seen later on in this report 10

10 Verbal reference by an employee of the bank. 14 15

Chapter 3

Settlement Risk at the Bank

In order to quantify the exposure of settlement risk at the bank, the financial instruments containing settlement risk must be identified. The bank currently offers a trading service for both domestic and international markets and small and larger customers. The financial instruments in which the bank is currently trading with/for customers are:

Shares • Bonds • Funds • Derivatives • Foreign Exchange • Moneymarket • The business center1 at the bank handles the settlements and has some procedures on how settlement of trades takes place. A trade request from a customer can come through Markets, VÍB, branches and online banking2. The settlement process for each ﬁnancial instrument is explained in next sections. With the objective of answering the important question for each instrument: "Is there a possibility that the bank might be exposed to settlement risk?". 1 Icelandic term is "Viðskiptaver" 2 Icelandic terms: "Markaðir", "VÍB: verðbréfa- og lífeyrisþjónusta", "Útibú" and "Netbanki" 16 Managing Settlement Risk in Banking

3.1 Example of Exposure to Settlement Risk at the Bank

This part was removed due to conﬁdentiality reasons.

3.2 Stocks

Trading of stocks (shares and bonds) does not differ on whether it is the domestic or international market. The bank takes on settlement risk due to securities settlement. There are two ways in which settlement risk can occur in these trades:

A customer buys stocks but doesn’t have the funds to pay for them on settlement • day.

A customer attempts to sell shares, but doesn’t have the stocks on a custody account • at the bank and doesn’t deliver the stocks on settlement day.

3.2.1 Domestic Market

The process flow for domestic shares and bonds is presented in figure 3.1. The first step of the process represents when a customer requests to buy/sell shares. A front line employee starts by checking the data from the customer to see if he/she has delivered the required data. If the customer is selling shares, the customer’s custody account is checked to see if the shares are there. If they are not the customer is asked to transfer the shares into the custody account at the bank. In step 4 the counterparty is informed about the current offer on exchange3 in case of stock exchange transactions. The customer should also be informed about fees and the settlement time (T+2 for example). After an order has been registered in the system (step 5) a broker forwards/announces the offer to the stock exchange or looks for external trades. Step 7 represents where the trade occurs. An offer is binding as soon as it has been accepted. A broker has to confirm the trade with a salesperson and put information in a system on amount/debit, fee, settlement date and salesperson. The final step is the settlement of transactions which takes place in the business center. The bank is exposed to settlement risk as soon as someone has agreed to sell/buy shares to one of the bank’s broker and until the business center has received shares/payment from the customer for the trade (figure 3.1).

3 The Icelandic stock exchange is called "Kauphöll" Þórdís Sara Ársælsdóttir 17

Figure 3.1: The process of trading shares and where exposure to settlement risk arises, domestic market. 18 Managing Settlement Risk in Banking

3.2.2 International Market

Foreign securities are booked on T+1 and settled on either T+2 or T+3. The process is very similar to the domestic one. On T+1 the stocks are transferred to/from the customer’s custody account and on T+2 the money transfer is settled. So the exposure to settlement risk starts as before: as soon as someone has agreed to sell/buy shares to one of the bank’s broker and until the business center has received shares/payment from the customer for the trade (ﬁgure 3.2). Þórdís Sara Ársælsdóttir 19

Figure 3.2: The process of trading shares and where exposure to settlement risk arises, international market. 20 Managing Settlement Risk in Banking

3.3 Funds

Domestic mutual funds have the settlement time T+1, T+2 and T+14. Every trade done with funds is processed the next working day. The cut off time for transactions through the online bank is 3 pm, transactions after that time are not processed until after 2 working days. In step 2 in ﬁgure 3.3 the employees of accounting of funds calculate the exchange rate of the funds and register it. Once funds have a calculated rate every trade of the day is booked. Once the rate has been calculated it is known how many units the customer should receive for the desired amount. The bank pays for every purchase in a fund and collects the amount from a customer afterwards. In step 5 everything is ﬁnished and in order and receipts are sent. The settlement, at the bank, is most commonly executed on T+2. So on T+2 the customer receives the units and his account is debited. Before the crisis in 2007 the bank worked on T+1, however they wanted to give foreign investors a chance since the international market works on T+2. Þórdís Sara Ársælsdóttir 21

Figure 3.3: The process of delivery of funds and where exposure to settlement risk arises, domestic market.

3.4 Derivatives

A derivative is a type of contract where the settlement is based on a speciﬁc factor during a certain period such as interest rate, exchange rate, currencies, stock price, stock index or commodity prices. Derivatives can be traded on a formal exchange or over the counter (OTC) to suit a customer requirement. The bank is always the counterparty to a derivative contract with its customers. The types of derivative contracts the bank is currently making are forward contracts and swaps. Options have recently been approved as a product in which the bank will be offering to its customers. The derivative contracts will be further explained in the following chapters. The process 22 Managing Settlement Risk in Banking

ﬂow of executing these contracts at the bank and how settlement risk can arise will be explained as well.

3.4.1 Forward Contracts

Forward contracts present a commitment for a counterparty to buy/sell an asset at a spe- ciﬁc time in the future for a certain price speciﬁed at the time where the contract is made. Forward contracts are settled at maturity and are mostly traded over-the-counter (OTC). A distinction should be made when pricing forwards depending on if the underlying asset is an investment or for consumption purposes. Investment assets are for example shares, bonds, currencies and some commodities. Consumption assets are mostly commodities such as oils, metals and types of foods. At maturity the asset holder delivers the asset in exchange for cash, delivery price (de- cided at the date of contract). In a short position the investor decides to sell the asset at future time and a long position presents the one deciding to buy an asset at future time. Contracts can also be settled in exchange for cash rather than delivery of an asset. This contract leads to a gain/loss for either counterparty due to the fact that the underlying asset might deviate from the contract price in either direction. Purchasing of an asset generally has three actions points which are:

Determining the price • Payment, they buyer of the asset pays the seller • The asset is transferred from the seller to the buyer • The three action points can take place at varying times, however in this case it is assumed that they can take place at two different times. Little t represents the time today and large T the future time. In a forward contract you pay at time T and receive the asset at time T. However there are other alternative ways of paying for and getting delivered an asset. The alternatives can be seen in table 3.1

Alternative Pay at Time Receive at Time Outright spot purchase t t Pre-paid forward contract t T Fully leveraged purchase T t Forward contract T T Table 3.1: Four alternatives of pay and delivery in forward contracts. Þórdís Sara Ársælsdóttir 23

The absence of arbitrage4 is necessary in order to price forward contracts. There is a way to fairly price an asset on future time T for a ﬁxed price today, t. However some assumptions have to be made such as the market being liquid, no transaction costs, same tax on all proﬁts, participants can lend and borrow at same rate and market participants can spot and make use of arbitrage possibilities. (Ólafsson, 2018).

The following notations will be used: t: Time today T: Time until delivery date in a forward contract (years)

F0: Forward price today r: Risk-free rate

S0: Spot price of the asset today

A forward contract with asset price S0 on an investment asset that provides no dividend payments (income) has the following relationship:

F = S erT (3.1) 0 0 ⇤

rT This relationship is based on arbitrage opportunities. Thus if F0 > S0 e , an investor making use of arbitrage opportunities could buy the asset and short a forward contracts rT on the asset. If F0 < S0 e similarly an investor could short the asset and make a long forward contract on the asset (Hull, 2012).

When an investment asset provides an income with present value I until maturity of the forward contract, the following formula fairly prices the derivative:

F =(S I)erT (3.2) 0 0

rT If F0 <(S0 - I)e a proﬁt could be locked in by an arbitrage investor by shorting the asset rT and taking the long position in a forward contract. However if F0 >(S0 - I)e a proﬁt could be made by buying the asset and shorting a forward contract on the asset (Hull, 2012).

4 Simultaneous purchase and sale of an asset to proﬁt from a price difference. 24 Managing Settlement Risk in Banking

With a known average yield per annum, q, on an asset during a forward contract’s life the forward price is: (Hull, 2012)

(r q)T F0 = S0e (3.3)

The big question is if the bank is exposed to settlement risk in forward contract with counterparties. The bank can be in a short or long position to a forward contract.

Short Position: In a short position the bank is obligated to sell the underlying asset/currency at a predeﬁned price, strike price. Let us say for example that the bank has made a forward contract to sell shares at a certain strike price. If the price of the share exceeds the strike price at maturity, the bank’s counterparty can purchase the shares and sell them again for a higher price. However if the price has decreased below the strike price at maturity, the counterparty is obliged to purchase the shares at the strike price, which is higher than the market price of the share. The bank is exposed to settlement risk if the bank were to deliver an asset/currency before a customer would have paid. If it were to happen that the counterparty of such a trade does not have the funds to go through with the trade, settlement risk occurs. The bank then has two options, one is to keep the shares and hope that the market price increases. The other is to replace the the current forward contract by selling the shares for a lower price on the market which also entails replacement cost risk.

Long Position: If the bank were to assume a long position he would agree to buy an underlying asset on a certain specified future date for a certain price. The bank’s counterparty would need to own the asset/currency at the future date specified. If the market price of the underlying asset has decreased throughout the life of the contract, the bank is obliged to buy the asset for the higher strike price. If the market price of the underlying asset has increased, the bank can purchase the asset on the strike price and sell again for market price and profit from the difference. However, if the bank pays the counterparty for the asset as per agreement and the counterparty fails to deliver it’s end of the contract settlement risk occurs. No replacement cost risk is included for the bank in this situation since the bank has no asset to replace. Þórdís Sara Ársælsdóttir 25

Foreign Exchange Forwards

The Bank is currently doing foreign exchange forward contracts with counterparties. In these type of contracts the bank and counterparties decide on a currency cross and pre- deﬁned exchange rate for a future maturity date. FX forwards can be settled either as outright forwards or as non-deliverable forwards. In outright forwards an actual exchange of currencies takes place. That is if the bank has obliged itself to deliver a certain amount of EUR in exchange for USD the bank, on settlement day, transfers the euros and the counterparty transfers the dollars. In non-deliverable forwards the bank and the counterparty would decide on one currency to settle on settlement day. If they would decide to settle in dollars at maturity date. Either the bank or the counterparty would transfer dollars depending on the difference in forward exchange rate and spot rate at maturity date.

Equity and Bond Forwards

How the bank could be exposed to settlement risk in equity and bond forwards will be explained in the results chapter.

3.4.2 Options

Although options have only recently become a product that the bank is offering, this chapter will be left in for possible further work. Options can be traded both on the OTC market and on exchanges. There are two types of options which are the call option and the put option. The ﬁrst one gives the holder the right to buy an asset on a certain day for a certain price. The latter one gives the holder the right to sell an asset on a certain day for a certain price. There is a slight difference between American and European options, thus the latter one can be exercised only on maturity day. Options, unlike forwards, gives the holder the right to do something. That is the holder is not obliged to sell/buy the underlying asset. Options entail a cost for the holder, that is he needs to pay for the right to hold the option. There are four types of participants to the option market and those are buyers of calls, sellers of calls, buyers of puts and sellers of puts. As before a long position refers to buyers of options and short position to sellers of options. Selling an option is also known as writing the option. The investor in a short position receives cash up front, with liabilities later on. Payoffs depending on position for european options can be seen in ﬁgure 3.4. The payoff for a long call increases when the price of a stock (ST ) is higher than the strike price (K) beaucse the investor has the option to buy the stocks for price K and can at maturity sell them for price ST . On the contrary 26 Managing Settlement Risk in Banking

the payoff for a short call decreases when ST >K. The payoff for a long put decreases until it reaches K and stays the same after that. In a long put, if ST >Kthe investor could buy stocks for the already agreed upon price K and sell them for the increased price

ST (Hull, 2012).

Figure 3.4: European options and payoffs depending on if it is a) long call, b) short call, c) long put or d) short put. Image from Options, Futures and Other Derivatives by John C. Hull.

The payoffs can be seen in table 3.2

Position Payoffs Long position (call option) max(S K, 0) T Short position (call option) max(S K, 0) = min(K S , 0) T T Long position (put option) max(K S , 0) T Short position (put option) max(K S , 0) = min(S K, 0) T T Table 3.2: Payoff depending on position in European call and put otpions.

Options need a price and there are six factors that affect the price of a stock option and they are:

1. The current stock price, S0 2. Strike price, K 3. Time to expiration, T 4. Volatility of the stock price, Þórdís Sara Ársælsdóttir 27

5. Risk-free interest rate, r 6. Dividends expected to be paid

In order to be able to price options, price ranges call and put options can have to eliminate arbitrage opportunities are looked at. Which involves establishment of lower and upper bounds for option prices. A distinction is made between American and European options and if the asset pays dividends or not.

The notations are: the current stock price S0, strike price of option K, time to expiration of option of an option T , stock price on expiration date ST , risk-free rate r, value of American call option to buy one share C, the same but put option to sell one share P , value of European call option to buy one share c and put option to sell p. An option price offers opportunities for arbitrageurs if an option price is below the lower bound or above the upper bound. An option can never have more value than the stock itself. Thus, the upper bound of an option price is the stock price.

c S and C S (3.4)  0  0

Equation 3.4 shows the upper bound for European and American call options. If these re- lationships were not true an arbitrageur could make an easy and risk less proﬁt by buying the stock an selling a call option. The lower bound for an American and European put option is displayed in equation 3.5 and 3.6 respectively. If these equalities were not true an arbitrageur could write an option and invest the remains at a risk free rate and make a riskless proﬁt. If the reader is interested in getting more knowledge on options, John C. Hull has a chapter dedicated to options in his book Options, Futures, and other Derivatives (Hull, 2012).

P K (3.5) 

rT p Ke (3.6) 

The bank can be in a short or long position to a call or put option. These four position will be looked into to see if the bank could be exposed to settlement risk in any of them. 28 Managing Settlement Risk in Banking

Long position (call option): If the bank takes on a long position to a call option he pays upfront for the option to buy the underlying asset at a strike price on a certain day in the future. So let’s say that day has come and the bank wants to exercise that right. The counterparty holds the asset and the bank the funds, if the bank were to transfer funds to the counterparty before receiving the asset he would expose himself to settlement risk.

Short position (call option): In a short position to a call option the bank is obligated to sell an underlying asset if the counterparty wants to exercise its right. If a counterparty exercises its right, the bank would be exposed to settlement risk if he would transfer the asset to the counterparty before receiving funds.

Long position (put option): In a long position to a put option the bank would have the right to sell an underlying asset at a strike price on a speciﬁc date. If the bank would like to exercise the right he would expose himself to settlement risk if he were to transfer the asset before receiving the funds from a counterparty.

Short position (put option): In a short position to a put option the bank would be obliged to buy an asset at the speciﬁed strike price and maturity date. If a counterparty would exercise its right, the bank would expose himself to settlement risk if he would transfer the funds before receiving the asset from the counterparty.

3.4.3 Swaps

Although swaps were not further looked into in this thesis the section will be left in for possible further work. A swap is a derivative contract between counterparties to exchange cash flows in the future. The contract should include the agreed upon exchange dates and how the cash flows should be calculated. The bank is currentlyl trading two types of swaps with customers/counterparties, interest rate swaps and currency swaps. Plain vanilla interest rate swap is the most common type of swap. In this type of a swap a company agrees to pay cash flows at a fixed rate in return for interest at a floating rate. (Hull, 2012) The latter one, currency swaps, involves exchanging principal and interest payments in one currency for principal and interest payments in another. The agreement requires the principal to be specified in each of the two currencies. The exchange of principal usually takes place at the beginning and at the end of the life of the swap. The principal amounts Þórdís Sara Ársælsdóttir 29 are usually chosen to be equivalent using the exchange rate at the beginning. At the end of life of the swap, those values may be quite different. If the reader is interested in getting more knowledge about interest rate and currency swaps, John C. Hull has a whole chapter dedicated to these kind of swaps in his book Options, Futures, and other Derivatives (Hull, 2012). The types of swaps the bank is currently trading are currency swaps and interest rate swaps. The counterparties to such trades are large and medium sized companies who want to control interest rate and foreign exchange risk. Once the day has come to settle, e.g. floating and fixed interest rate between the bank and a customer, the bank transfers the amount it owes the counterparty. At that point the bank has exposed himself to settlement risk. However, since most of the counterparties are the bank’s customers they have an account at the bank. Which enables the bank to use netting as a way to mitigate the settlement risk. Netting means that the difference between what the bank owes a counterparty and what a counterparty owes the bank is the only amount transferred. In figure 3.5 it can be seen how payments occur in a swap contract between the bank and a counterparty. The bank takes on a floating rate loan and the counterparty starts paying fixed rate payments instead. As mentioned, the bank is exposed to settlement risk if he would pay a counterparty the fixed rate payments before receiving the floating rate payments. The bank can also be exposed to some residual settlement risk even if the bank uses netting if the customer would owe the bank a net amount.

Figure 3.5: How settlement risk can occur when Íslandsbanki is in a forward swap contract with a counterparty

3.5 Foreign Exchange

Foreign exchange settlement risk was explained in details in chapter 2. However it will be explained in the chapter containing results how the bank could be exposed to settlement risk. 30 31

Chapter 4

Methods

The thesis was based on a lot of data from various sources. This chapter therefore explains what data was used, from where it was retrieved and so on. This chapter also attempts to explain the fundamental mathematical techniques applied to quantify settlement risk.

4.1 Data

In order to quantify the bank’s exposure to settlement risk, data is needed. Data for stocks, derivatives and foreign exchange transactions was treated separately. The reason for that is due to the nature of those instruments but foremost due to how the data is kept in the bank’s databases. The data is kept in different systems depending on instrument.

4.1.1 Stocks

Data for every stock transaction for the year 2017 was retrieved from the bank’s databases. The information retrieved contains parameters such as

Total amount traded • Stock type (shares, bonds or funds) • Name of stock • Counterparty • Transaction date (T ) • 32 Managing Settlement Risk in Banking

Figure 4.1: How stock trades can either go through or not at after the bank has purchased the stock, thus leading to settlement risk

Settlement date (T + x) • Trading reversed (yes or no) • Unique trading number • The data doesn’t indicate directly if a counterparty has defaulted, thus exercising settlement risk. However the column, Trading reversed (yes or no), indicates if the trade was reversed due to some reason. The reason a trade is reversed can be multiple, a common one is that there was some error in the trade. If there was an error in the trade an employee of the bank would in most cases reverse a trade and put in the system a new trade. It is possible to track those trades and filter them from other reversed trades. Thus by compar- ing amounts of reversed trades and non reversed trades and if the same amount occurs in both cases it’s most likely just en error fix. Figure 4.1 shows the explanation in a figure, thus how stock trades can either go through or not after the bank has purchased the stock, thus leading to a possible loss for the bank in which exposure to settlement risk would have occurred.

4.1.2 Derivatives

Data was retrieved for the following derivative types: Þórdís Sara Ársælsdóttir 33

Foreign Exchange Forward (FX Forward) • Currency Interest Rate Swap Deal (CIRS, Foreign Exchange) • Interest Rate Swap (IRS) • Equity Forward • Bond Forward • Equity and bond forwards include the same information which are:

Currency ID: Icelandic Krona in all cases (ISK). PNL: The Banks proﬁt or loss in ISK. RB Time Stamp: Date and time of when the transactions actually occur. Counterparty: The counterparty to a trade. Underlying asset: The underlying asset to a trade either an equity (stock or portfolio) or bond. Buy/Sell: An indication of which position the bank holds, the buyer or seller of the underlying asset. Quantity: How many shares of the underlying asset is being traded. Price: Price per share. Maturity Date: Expected settlement date at the beginning of the contract or in better words, maturity date.

FX forwards, CIRS and IRS all include the same information which are:

FO Deal ID: Contract Identiﬁcation. Counterparty: The counterparty to a trade. Short name: Identiﬁcation of the counterparty in the Bank’s database. Amount in foreign currency: Total amount in the foreign currency. If the trade does not include foreign exchange the ISK amount will also appear here. Amount in Icelandic Krona (ISK): The amount in ISK. Currency: The currency paid out or received. Currency Cross: The currency cross to a trade (if any), EUR/USD for example. Rate: The rate of exchange for a currency cross (if any). Payment Date: Expected settlement date at the beginning of the contract or in other words, payment date. Description: Type of deal. RB Time Stamp: Date and time of when the transactions actually occur. 34 Managing Settlement Risk in Banking

Days exceeding or days before: The number of days which the payment occurs either before or after maturity date.

4.1.3 Foreign Exchange

Data was retrieved for foreign exchange spot deals. The data for the spot deals is the same as for FX forwards, CIRS and IRS.

4.1.4 Historical Data on Shares and Funds

Data was retrieved for the shares present in table 4.1 in the year 2017. Historical prices for the Icelandic shares was retrieved from Kauphöllin1. The only variable used was the closing price of the stock trade. The historical prices of the foreign shares were mostly retrieved from Yahoo Finance.2

1 Nasdaq Nordic: http://www.nasdaqomxnordic.com/ 2 https://ﬁnance.yahoo.com/ Þórdís Sara Ársælsdóttir 35

Icelandic Shares Eik Fasteignafélag Tryggingamiðstöðin hf. Vátryggingafélag Íslands Eimskipafélag Íslands Fjarskipti hf. Hagar hf. HB Grandi hf. Icelandair Group hf. Marel hf. N1 Reginn Reitir Fasteignafélag hf. Síminn hf. Skeljungur hf. Sjóvá-Almennar Tryggingar hf. Össur hf. Amazon Com Inc. Apple Inc. Barclays plc Cannabis wheaton income corp Century aluminium company Extreme networks inc. Ishares barclays tips bond Ishares core MSCI EAFE ETF Ishares core MSCI emerging mar Ishares us energy etf LG display co ltd. Netﬂix inc. Nividia corp. Nova nordisk A/S - B NovaTek PJSC Petroleum Geo-Services SPDR Dow Jones Industrial Aver Strax AB Tesla Motors inc The walt disney co. Ultra QQQ proshares United states steel corp. Table 4.1: The shares, for which data was retrieved from Kauphöllin and Yahoo Finance for the year 2017 with 250 business days.

Funds

Data was retrieved for the funds present in table 4.2 from various sources3 3 Alda Funds retrieved directly from Alda by e-mail Gamma funds from datamarket: https://datamarket.com/ 36 Managing Settlement Risk in Banking

Funds Alda Hlutabréf Alda Ríkisverðbréf löng Gamma Government Bond Fund Gamma Equity IS Sértryggð skuldabréf VTR IS Eignasafn IS Einkasafn C (fl. A) IS Einkasafn C (fl. B) IS Einkasafn D (fl. A) IS Einkasafn D (fl. B) IS Einkasafn E (fl. B) IS Einkasafn Erlent (ISK fl.A) IS Einkasafn Erlent (USD fl.A) IS Einkasafn Erlent (USD fl.B) IS Fókus-vextir IS Hlutabréfasjóður IS Lausafjársafn IS Ríkisskuldabréf óverðtryggð IS Skuldabréfasafn IS Veltusafn Vanguard Global Stock Index Vanguard Emerging Markets Stk Vanguard European Stock Index Vanguar Global Enhanced Eq. Fund Vanguard US Ush Term Bond Fund Vanguard US500 Stock Index BGF Global Allocation Fund Capital Group New Perspective Henderson European Focus Fund Aberdeen Global - World Eq. Table 4.2: The funds, for which data was retrieved from various sources for the year 2017 with 250 business days.

4.1.5 Historical Data for Offered Interbank Rate Depending on Cur- rency

The offered interbank interest rate was retrieved for the various currencies, traded with in foreign exchange forwards. The interest rates are presented in table 4.3.4

Íslandssjóðir directly from Íslandssjóðir by e-mail BGF Global Allocation Fund retrieved from www.blackrock.com The rest was retrieved from www.ﬁnance.yahoo.com 4 ISK REIBOR retrieved the Central Bank of Iceland, www.sedlabanki.is DKK CIBOR and SEK STIBOR retrieved www.nasdaqomxnordic.com Þórdís Sara Ársælsdóttir 37

Currency Interest Rate EUR LIBOR GBP LIBOR USD LIBOR ISK REIBOR DKK CIBOR NOK OIBOR/NIBOR SEK STIBOR Table 4.3: Interest rates retrieved for each currency.

4.2 Geometric Brownian Motion

The probability method as led out by (Chin, Nel, & Ólafsson, 2014) will be used to estimate the probability of S(T ) S(t)(1 + c ) for ﬁnancial instruments where the  r underlying is an asset. We make the assumption that asset prices follow a Geometric Brownian Motion Process where µ is the drift, the volatility and W is a Wiener Process.

dS(t)=µS(t)dt + S(t)dW (t) (4.1)

To solve this equation we follow the standard procedure and introduce

S f(S)=logS(t); =0 (4.2) t

Then, using Taylor expanding f(x) and using dW 2 = dt we ﬁnd

2 dlogS(t)=(µ )dt + dW (t) (4.3) 2

After integrating both sides from t to T we ﬁnd

2 logS(T )=logS(t)+(µ )(T t)+(W (T ) W (t)) (4.4) 2

For the expectation value and variance we have

NOK NIBOR retrieved Oslo Bors, www.oslobors.no EUR, GBP, USD LIBOR retrieved www.global-rates.com 38 Managing Settlement Risk in Banking

2 E(logS(T )) = logS(t)+(µ )(T t); var(logS(T )) = 2(T t) (4.5) 2 and therefore,

2 logS(T ) N(logS(t)+(µ )(T t), 2(T t)) (4.6) ⇠ 2

After applying the exp-function to both sides of equation 4.4 we ﬁnd

2 S(T )=S(t)exp((µ )(T t)+(W (T ) W (t))) (4.7) 2

Now it follows from the properties of the normal distribution that

2 (log( s ) (µ )(T t)) S(t) 2 (S(T ) s)=P (⌘ pT t )=   2 (4.8) (log( s ) (µ )(T t)) S(t) 2 N( pT t ) where ⌘ is the standardized norma probability density function and N() is the standardized normal cumulative distribution.

(Chin et al., 2014)

4.3 Maximum-Likelihood Estimation Method

The maximum-likelihood estimation method as led out by (Chin, Nel, & Ólafsson, 2017) will be used to calculate the historical estimates of the drift µ and volatility . The likelihood function is the joint density of

S S S log( t+t ),log( t+2t ),...,log( t+Nt ) (4.9) St St+t St+(N 1)t which is the product of their marginal densities

S log( t+it ) (µ 1 2)t N 1 1 St+(i 1)t 2 2 (µ, )= exp( ( ) )= i=1 p2⇡t 2 pt (4.10) R (µ 1 2)t Q N 1 exp( 1 ( i 2 )) i=1 p2⇡t 2 pt Q Þórdís Sara Ársælsdóttir 39 where St+it Ri = log( ),i=1, 2,...,N (4.11) St+(i 1)t Taking the log-likelihood

N 1 N 1 log`(µ, )= Nlog log(2⇡t) (R (µ 2)t)2 (4.12) 2 22t i 2 Xi=1 and partial differentials with respect to µ and ,

log` 1 N 1 = (R (µ 2)t) (4.13) µ 2 i 2 Xi=1

log` N 1 N 1 1 N 1 = + (R (µ 2)t)2 (R (µ 2)t) (4.14) 3t i 2 i 2 Xi=1 Xi=1 and by setting the partial differentials with respect to µ and equal to zero, the maximum- likelihood estimates µˆ and ˆ satisfy

1 (ˆµ ˆ)t = R¯ (4.15) 2 and

N 1 N 1 N + (R R¯)2 (R R¯)=0 (4.16) ˆ ˆ3t i ˆ i Xi=1 Xi=1 where

1 N R¯ = R (4.17) N i Xi=1 Thus, the parameters µ and can be estimated with historical data by using

1 1 N µˆ = (R¯ + (R R¯)2) (4.18) t 2N i Xi=1 40 Managing Settlement Risk in Banking and 1 N ¯ 2 ˆ = v (Ri R) (4.19) uNt u Xi=1 t (Chin et al., 2017)

4.4 Probability of FX Rate Being Smaller than Some Value K Using Geometric Brownian Motion

The following will be used to calculate the probability that the FX rate at a future time T is smaller than some value K.

Let X(t)=X(t)d,f be the amount of domestic currency (d) per unit of foreign currency (f). It is assumed that the foreign exchange rate follows the geometric Brownian motion process,

dX(t)=(r r )X(t)dt + (W (T ) W (t)) (4.20) d f X where rd and rf are the domestic and foreign interest rates respectively. Taken as Libor rates or Ribor rates in Iceland. X is the annualized volatility of the FX rate X(t). By applying Ito’s Lemma on the stochastic differential equation 4.20 it can be solved to ﬁnd

r (t,T ) r (t,T ))(T t)+ (W (T ) W (t)) X(T )=X(t)e d f X (4.21)

Where r (t, T ) and r (t, T ) are the Libor rates for the term T t. d f The probability that the FX rate X(T ) at the future time T is smaller than some value K is given by the expression,

2 K x log( ) (rd rf + )(T t) P (X(T ) K)=N( X(T ) 2 ) (4.22)  pT t X Where N is the standardized cumulative normal distribution. Whether the bank would gain our lose in case of a settlement failure/default depends on whether the FX rate is below or above the rate the bank had to pay for the currency. (Chin et al., 2014). 41

Chapter 5

Results

The beginning of this chapter covers statistical information on settlement risk for the ﬁ- nancial instruments in which the bank is trading. That is, exposure time or settlement time, underlying amounts and so forth.

The second half is dedicated to the quantiﬁcation of the settlement risk exposure. Where fundamental mathematical techniques applied are based on the assumption that prices follow a geometric Brownian motion process. We then apply Ito’s Lemma, arbitrage techniques and basic probabilistic methods to quantify the settlement risk exposure.

5.1 Statistics

5.1.1 Stocks

To get a feel for the data, amounts traded by customers will be displayed by the use of histograms in hopes of identifying patterns. The nature of the data makes it difﬁcult to present it in a histogram as it is. Thus, a histogram of the data is presented on a logarithmic scale of 10 in ﬁgure 5.1. The trade count is displayed on the y-axis and the log-10 value of amounts on x-axis. The amounts traded follow a somewhat normal distribution except for three large bins on the left hand side of the graph.

Figure 5.2 shows the total amount traded by counterparties with shares, bonds and funds per settlement time. The highest total amount is associated with the settlement time T+2. In second place is T+1 and in third place is the settlement time T+4. It is interesting to see that a fair amount is being traded on settlement times T+5, T+6 and T+7. The 42 Managing Settlement Risk in Banking

Figure 5.1: A histogram of the amounts traded on a log-10 scale for every stock type (with 80 bins). settlement risk rises with increased settlement times.(Borio et al., 2008). Thus, the bank should always look for ways to minimize settlement times in every trade.

Figure 5.2: Total amount traded with the settlement time ranging from 0-21 days. Þórdís Sara Ársælsdóttir 43

It is interesting to see in ﬁgure 5.3 how the amounts traded with counterparties differ depending on type. The types are shares, bonds and funds. Bonds are traded less than shares and funds, but they tend to be traded with higher amounts. Shares are more commonly traded than bonds but less traded than funds, however shares tend to be traded with lower amounts. Funds are the most common and the most traded within lower amounts. That is probably due to the fact that inexperienced and economically worse positioned counterparties are directed to invest in funds.

Figure 5.3: A histogram of the amounts traded on a log-10 scale for every stock type (with 80 bins).

A histogram of reversed trades on a log-10 scale ﬁltered by stock type can be seen in ﬁgure 5.4. The distribution is somewhat normally distributed. 44 Managing Settlement Risk in Banking

Figure 5.4: A histogram of reversed trades on a log-10 scale for every stock type (with 50 bins).

5.1.2 Derivatives

This section covers derivatives where the underlying asset is anything but a currency. The ones covered in this thesis are equity and bond forwards. As stated in earlier chapters the bank is also currently trading interest rate swaps and options recently got approved as products at the bank.

Equity and Bond Forwards

The maturity date and the actual settlement date for the equity and bond forwards are included in the data. Thus, it was possible to generate how many days before/after maturity date the contracts are settled. The average time in days can be seen in table 5.1. The equity and bond forwards are settled on average about 3 and 1 days, respectively, before the maturity date.

The bank mitigates settlement risk in equity and bond forwards by netting the trades. That is, instead of an actual delivery of the asset and cash, the net proﬁt or loss is paid Þórdís Sara Ársælsdóttir 45

Forward Contract Days before/after maturity, trades settled (days) Equity Forward -2.91 Bond Forward -1.29 Table 5.1: Average time (in days) it takes to settle equity and bond forwards, thus settlement time (T + x) from maturity date (T ) out by either the bank or counterparty. If the proﬁt or loss amount (referred to as PNL) is negative, it means that the bank owes the counterparty at maturity. However if the PNL amount is positive it is the net amount in which the counterparty owes the bank. Only 100 out of 1131 of the trades have a positive PNL amount, meaning that the bank could have been exposed to residual settlement risk in 8.8% of trades.

The net amount paid by the bank/counterparty days before/after maturity date is presented in ﬁgure 5.5. As can be seen the equity and bond forwards are mostly settled before or on maturity date and the net amount to be paid by the bank exceeds the net amount to be received by counterparties.

Figure 5.5: Equity and bond forwards where the net amount paid either by the bank (negative) or counterparty (positive) is on y-axis. X-axis represents days before/after maturity date where the forwards are completed.

The residual settlement risk can be seen in figure 5.6. The figure shows the log10 value of the net amounts counterparties owe the bank, filtered by forward type (equity or bond). 46 Managing Settlement Risk in Banking

The equity forwards clearly include more residual settlement risk than the bond forwards.

Figure 5.6: Histogram of the log10 value of net amounts of forwards where the counterparty owes the bank at maturity date.

Figure 5.7 represents when, the trades including residual settlement risk, are settled. The contracts are mostly settled before and on maturity date. Þórdís Sara Ársælsdóttir 47

Figure 5.7: The net amount counterparties owe the bank on y-axis and day before/after maturity date on x-axis.

5.1.3 Foreign Exchange

This section covers all instruments where the underlying asset is a currency. That includes foreign exchange forward contracts and foreign exchange spot contracts.

Foreign Exchange Forward Contracts

The data for foreign exchange forwards included 900 rows of data at ﬁrst. However some rows were duplicated and after cleaning the data and getting rid of duplicates the number of rows decreased to approximately 590 rows. A foreign exchange forward contract includes both sides of the contract, that is the amount transferred by the bank and the amount received from counterparty. Thus, 590 rows of data gives approximately 295 forward contracts. The contracts include (in most cases) the time stamp of when the transactions occur which makes it possible to see at what date and time the bank pays the counterparty and gets paid from the counterparty. A FX forward contract includes two rows where the exchange rate of the currency cross at maturity date is stated and the amount paid/received in both currencies. The FX forwards are currently traded with the underlying currency crosses: 48 Managing Settlement Risk in Banking

DKK/ISK • EUR/ISK • EUR/NOK • GBP/ISK • GBP/USD • ISK/DKK • ISK/EUR • ISK/GBP • ISK/NOK • ISK/SEK • ISK/USD • NOK/ISK • SEK/ISK • USD/ISK • The foreign exchange forward contracts were mostly settled simultaneously. The transactions differed only by split seconds in most cases and even so the bank made sure to receive it’s end of the currency cross before transferring to the counterparty. There are five contracts where the bank paid before receiving funds from the counterparty. The settlement risk exposure time in these instances was about a minute to five minutes maximum. The five registered instances are presented in table 5.2. If we take the first instance as an example, the bank paid the counterparty to that contract 303.5 million ISK (forward rate) before receiving 20 million NOK (260 million ISK on spot rate at maturity). Þórdís Sara Ársælsdóttir 49

Table 5.2: The ﬁve instances where the Bank was exposed to settlement risk for 1-5 minutes in FX forwards. Instance Amount in Currency Amount in ISK Currency Currency Cross 1 20.000.000 260.040.000 NOK NOK/ISK 1 -303.500.000 -303.500.000 ISK NOK/ISK 2 3.000.000 312.180.000 USD USD/ISK 2 -327.360.000 -327.360.000 ISK USD/ISK 3 100.000 12.435.000 EUR EUR/ISK 3 -11.808.000 -11.808.000 ISK EUR/ISK 4 75.976 920.832 SEK SEK/ISK 4 -1.000.000 -1.000.000 ISK SEK/ISK 5 781.616 9.709.238 SEK SEK/ISK 5 -10.000.000 -10.000.000 ISK SEK/ISK

Foreign Exchange Spot Contracts

The initial hypothesis was that the bank is exposed to settlement risk when trading with foreign counterparties larger than the bank. However the data cannot indicate whether that hypothesis is true or not. The reason for that is that the time stamps, of when transactions occur in a spot contract between the bank and the larger counterparties, are missing. Those missing time stamps occur in another manner and are stored differently, they are so called swift transactions. The swift transactions are in reality a message where the bank instructs a nostro bank to transfer currency to a foreign account. The data does however include time stamps of transaction between the bank and counterparties who hold domestic accounts. The data includes about 13.462 foreign exchange spot deals. There are 5908 FX spot deals which contain the RB time stamp for both transactions (the bank’s and the counterparty’s). The bank was exposed to settlement risk in 18 FX spot contracts or 0.30% of the total spot contracts that include time stamps. The average exposure amount is 105 MISK with the exposure time ranging from 1 second to 4 days.

5.2 Fitting the Parameters

The parameters µˆ and ˆ were ﬁtted in matlab by using the maximum-likelihood estimation method. To be precise formulas 4.11, 4.17, 4.18 and 4.19 were used. 50 Managing Settlement Risk in Banking

5.2.1 Shares

The reversed trades with shares, for which the parameters µˆ and ˆ were ﬁtted, are presented in table 5.3.

Stock µˆ ˆ Eik Fasteignafélag 0.0771 0.2033 Tryggingamiðstöðin hf. 0.1782 0.1862 Vátryggingafélag Íslands 0.2586 0.1979 Eimskipafélag Íslands -0.2404 0.2049 Fjarskipti hf. 0.2957 0.1881 Hagar hf. -0.3872 0.2585 HB Grandi hf. 0.3249 0.2381 Icelandair Group hf. -0.3797 0.4282 Marel hf. 0.2755 0.2012 N1 -0.1041 0.2936 Reginn -0.0074 0.1881 Reitir Fasteignafélag hf. -0.0839 0.1730 Síminn hf. 0.2878 0.2011 Skeljungur hf. -0.0186 0.2506 Sjóvá-Almennar Tryggingar hf. 0.0845 0.1912 Össur hf. 0.0918 0.2475 Amazon Com inc 0.4602 0.2041 Apple Inc 0.3917 0.1753 Barclays plc -0.1087 0.2160 Cannabis wheaton income corp 6.1355 1.9098 Century aluminium company 1.0295 0.6309 Extreme networks inc. 0.9645 0.4050 Ishares barclays tips bond 0.0077 0.0358 Ishares core MSCI EAFE ETF 0.2062 0.0803 Ishares core MSCI emerging mar 0.2892 0.1188 Ishares us energy etf -0.0493 0.1426 LG display co ltd. 0.0944 0.3156 Netﬂix inc 0.4466 0.2733 Nividia corp. 0.7181 0.3947 Nova nordisk A/S - B 0.4407 0.2607 NovaTek PJSC -0.1217 0.2104 Petroleum Geo-Services -0.4528 0.5314 SPDR Dow Jones Industrial Aver 0.2226 0.0645 Strax AB 0.0764 0.3296 Tesla Motors inc 0.4230 0.3520 The walt disney co. 0.0248 0.1513 Ultra QQQ proshares 0.5359 0.2033 United states steel corp. 0.1724 0.5634 Table 5.3: The ﬁtted parameters µˆ and ˆ for Icelandic and foreign stocks on market. Þórdís Sara Ársælsdóttir 51

5.2.2 Funds

The reversed trades with funds, for which the parameters µˆ and ˆ were ﬁtted, are presented in table 5.3.

Fund µˆ ˆ Alda Hlutabréf -0.0625 0.1682 Alda Ríkisverðbréf löng 0.0747 0.0285 Gamma Government Bond Fund 0.0934 0.0438 Gamma Equity 0.0230 0.1395 IS Sértryggð skuldabréf VTR 0.0745 0.0161 IS Eignasafn 0.0389 0.0298 IS Einkasafn C (fl. A) 0.0347 0.0318 IS Einkasafn C (fl. B) 0.0411 0.0318 IS Einkasafn D (fl. A) 0.0232 0.0486 IS Einkasafn D (fl. B) 0.0297 0.0486 IS Einkasafn E (fl. B) 0.0111 0.0744 IS Einkasafn Erlent (ISK fl.A) 0.1029 0.1405 IS Einkasafn Erlent (USD fl.A) 0.1786 0.0412 IS Einkasafn Erlent (USD fl.B) 0.1848 0.0412 IS Fókus-vextir 0.0673 0.0208 IS Hlutabréfasjóður -0.0441 0.1370 IS Lausafjársafn 0.0459 0.0020 IS Ríkisskuldabréf óverðtryggð 0.0414 0.0410 IS Skuldabréfasafn 0.0674 0.0105 IS Veltusafn 0.0473 0.0046 Vanguard Global Stock Index 0.1886 0.0655 Vanguard Emerging Markets Stk 0.2438 0.0896 Vanguard European Stock Index 0.2110 0.0902 Vanguar Global Enhanced Eq. Fund 0.2221 0.0666 Vanguard US Ush Term Bond Fund -0.0020 0.0063 Vanguard US500 Stock Index 0.1718 0.0677 BGF Global Allocation Fund 0.1086 0.0373 Capital Group New Perspective 0.1991 0.0905 Henderson European Focus Fund 0.1310 0.0954 Aberdeen Global - World Eq. 0.1251 0.1073 Table 5.4: The fitted parameters µˆ and ˆ for the funds the bank trades for customers. 52 Managing Settlement Risk in Banking

5.2.3 FX Rates

The annualized volatility for the FX rates X(t), X , was calculated in Matlab by using the maximum likelihood estimation. The results can be seen in table 5.5.

Currency Cross X DKK/ISK 0.0322 EUR/ISK 0.0323 EUR/NOK 0.0765 GBP/ISK 0.1208 GBP/USD 0.1443 NOK/ISK 0.0796 SEK/ISK 0.0610 USD/ISK 0.0865 Table 5.5: Annualized volatility for the foreign exchange rates X(t) (maximum likelihood estimation method, year 2016). Þórdís Sara Ársælsdóttir 53

5.3 Probability that the Stock Price at Time T is Less than at Time t Plus Fees

5.3.1 Stocks

The probability that the price at time T (settlement date), for shares and funds, is less than the price at time t (transaction date) plus the fees for the bank of trading through exchange was calculated (5.1). The probability was calculated by the use of equation 4.8 where the inputs µˆ and ˆ were inputs as well as the price at time t, days until maturity and cost of purchasing/selling stock (fees) or the cost rate, cr, which is ﬁxed at 0.75% throughout the rest of the thesis.

P (S(T ) S(t)(1 + c )) (5.1)  r

It is more favorable for the bank if the probability of equation 5.1 is low. Let’s say that a counterparty fails to settle and the bank needs to replace the existing trade. If the price at time T is lower than at time t plus the fee, the bank needs to replace the trade and will encounter replacement cost risk. Equation 4.8 will not work in cases where the settlement time is 0 days, as expected.

The average probability of the bank incurring loss for the reversed transactions of the Icelandic shares is 38.18%. Figure 5.8 represents a histogram of the probability of S(T )  S(t)(1 + cr) ﬁltered by Icelandic stock type.

Based on the calculations the bank was likely to lose money on the reversed trades for the Icelandic stock types:

Icelandic Stock 2 • Icelandic Stock 4 • Icelandic Stock 5 • Icelandic Stock 7 • Icelandic Stock 9 • Icelandic Stock 12 • 54 Managing Settlement Risk in Banking

Figure 5.8: Histogram of the probability of S(T ) S(t)(1 + c ) for Icelandic shares,  r where the trade count is represented on the y-axis and the probability on the x-axis.

Icelandic Stock 8 • The log10 amounts of reversed trades ﬁltered by stock type is presented in ﬁgure 5.9. Ice- landic Stock 5 was the second most traded stock (based on amount) within reversed trades and had 100% probability of being less valuable at settlement date (T + x) compared to transaction date (T ). Þórdís Sara Ársælsdóttir 55

Figure 5.9: Log10 value of amounts of reversed trades ﬁltered on Icelandic stock type.

The same calculations were done for the reversed foreign shares. Thus the probability that the bank would lose money in case of exposure to settlement risk filtered by foreign stock type can be seen in figure 5.10. Based on the figure the following stocks had about 100% probability of being less valuable at settlement time.

Foreign Stock 3 • Foreign Stock 13 • Foreign Stock 14 • Foreign Stock 9 • The other stocks in ﬁgure 5.10 have 0% probabilities of being less valuable at settlement time except for Foreign Stock 18 and Foreign Stock 6 which have 9.81% and 12.89% probabilities respectively.

There are four stocks that stand out in ﬁgure 5.11, that is being the stocks traded the most based on amount. Those are Foreign Stock 1, Foreign Stock 5, Foreign Stock 10 and Foreign Stock 16. All of those stocks have 0% probabilities of resulting in loss for the bank when exposed to settlement risk. 56 Managing Settlement Risk in Banking

Figure 5.10: Histogram of the probability of S(T ) S(t)(1 + c ) for foreign shares,  r where the trade count is represented on the y-axis and the probability on the x-axis.

Figure 5.11: Log10 value of amounts of reversed trades ﬁltered on foreign stock type. Þórdís Sara Ársælsdóttir 57

Funds

Figure 5.12 represents a histogram of the probability of S(T ) S(t)(1 + c ) ﬁltered  r on the reversed Icelandic funds. Based on the ﬁgure the bank was likely to incur loss if exposed to settlement risk on the reversed trades for the following funds:

Icelandic Fund 1 • Icelandic Fund 15 • The funds Icelandic Fund 3 and Icelandic Fund 10 have 5.74% and 11.96% probabilities respectively. The rest of the Icelandic funds all have approximately 0% probabilities.

Figure 5.12: Histogram of the probability of S(T ) S(t)(1 + c ) for Icelandic shares,  r where the trade count is represented on the y-axis and the probability on the x-axis.

Based on ﬁgure 5.13, the total amount of the reversed trades for Icelandic Fund 1 in the year 2017 was low. However the total amount of reversed trades for Icelandic Fund 15 was a bit more in the year 2017. Icelandic Fund 16 was by far the most traded fund in the year 2017 based on amount. 58 Managing Settlement Risk in Banking

Figure 5.13: Log10 value of amounts of reversed trades ﬁltered on Icelandic fund type.

Now to foreign funds, the probability of loss for the bank if exposed to settlement risk is represented in ﬁgure 5.14. There is one fund with 100% probability which is the fund Foreign Fund 9. It can be seen in ﬁgure 5.15 that the total amount of the reversed trades Foreign Fund 9 in the year 2017 was low compared to the other funds. Þórdís Sara Ársælsdóttir 59

Figure 5.14: Histogram of the probability of S(T ) S(t)(1 + c ) for foreign funds,  r where the trade count is represented on the y-axis and the probability on the x-axis

Figure 5.15: Log10 value of amounts of reversed trades ﬁltered on foreign fund type.

5.3.2 Equity Forwards

Some assumptions had to be made for equity forwards, for instance the contract dates were missing. Therefore the lifetimes of the equity forwards had to be assumed. The 60 Managing Settlement Risk in Banking equity forward contracts were assigned random lifetimes ranging from 4-12 months. The ﬁtted parameters in table 5.3 for the Icelandic stocks were used as well as formula 4.8. The Bank can take two positions to the equity forward contracts, to be the buyer or seller of the underlying asset. It is not straightforward to recognize if it is better for the bank if the probability of S(T ) S(t)(1 + c ) is high or low when exposed to settlement risk.  r Thus, the different scenarios are presented in ﬁgure 5.16. Under normal circumstances, if the bank is the buyer in an equity forward contract he would like the probability of S(T ) S(t)(1 + c ) to be low. However, if the bank were  r exposed to settlement risk and S(T ) S(t)(1 + c ) the bank would possibly lose the  r principal amount and miss out on opportunity cost.

If the bank is the seller of the underlying asset in an equity forward contract, owns the stock on hand and is exposed to settlement risk. It would be better for the bank if the probability of S(T ) S(t)(1 + c ) is low. If the counterparty would fail to settle leaving  r the bank with an asset he needs to replace, it is straightforward that S(T ) >S(t) would be more favorable. Last but not least the bank can also be the seller and not own the stock on hand and in that case the bank would like the probability to be high. However it is safe to say that the bank does never not own the stock on hand. The equity forward contracts are protected by the bank’s brokerage department where they purchase the underlying stock simultaneously as contracts are ﬁnal.

The bank takes the position of being the seller in majority of the trades, ﬁgure 5.17. As stated earlier, it’s more favorable for the bank if the probability of S(T ) S(t)(1 + c )  r is low (if exposed to settlement risk) if the bank owns the stock on hand. Based on ﬁgure 5.17 the probability is distributed over the whole range from 0-100% with the average probability being 50.87%.

Figure 5.18 shows the probability of S(T ) S(t)(1 + c ) in instances where the bank  r holds the buyer position. It is difﬁcult to say whether it’s better or not for the bank that the probability of S(T ) S(t)(1 + c ) is high or low when exposed to settlement risk in  r the buyer position. The bank would lose the principal amount if he paid the counterparty before receiving the asset. If the counterparty would fail to oblige with the contract after the bank had already paid the counterparty. Let’s say the counterparty would pay the bank back the principal amount. The bank would have "dodged a bullet" in cases where the price had decreased but not in cases where the price of the stock had increased.

Figure 5.19 displays the probability of S(T ) S(t)(1 + c ) in the instances where the  r bank holds the seller position. It was established earlier that when the bank holds a seller Þórdís Sara Ársælsdóttir 61

Figure 5.16: A tree explaining the scenarios in equity forwards the bank can be in and when it’s better if the probability of S(T ) S(t)(1 + c ) are high or low.  r position he owns the stock on hand. If the bank is exposed to settlement risk holding the seller position, stocks having low probabilities of S(T ) S(t)(1 + c ) are more  r preferable. With that being said, based on ﬁgure 5.19 stocks such as:

Icelandic Stock 10 • Icelandic Stock 14 • Icelandic Stock 6 • Icelandic Stock 3 • Icelandic Stock 13 • should be categorized as less risky for the bank.

The bank could categorize the stocks into ﬁve risk categories where category one is the least risky and ﬁve being the most risky. The bank could take an extra fee for the added risk of entering into equity forward contracts with the higher risk counterparties based on the underlying stock’s risk category. It should be noted that the risk categories are based 62 Managing Settlement Risk in Banking

Figure 5.17: The ratio between the bank’s two positions of being the buyer or seller.

Figure 5.18: The probability that S(T ) S(t)(1+c ) for equity forwards where the bank  r holds the buyer position. Þórdís Sara Ársælsdóttir 63

Figure 5.19: The probability that S(T ) S(t)(1+c ) for equity forwards where the bank  r holds the seller position. on historical data for the stocks. So even though Icelandic Stock 10 is in category one based on this data it can later on fall in other categories. The number of categories can also change based on the data’s pattern. The probability pattern in ﬁgure 5.19 indicates ﬁve categories but that could change.

Risk Category Stocks 1 Icelandic Stock 10 Icelandic Stock 14 Icelandic Stock 6 Icelandic Stock 3 Icelandic Stock 13 2 Icelandic Stock 11 Icelandic Stock 1 3 Icelandic Stock 8 Icelandic Stock 12 4 Icelandic Stock 7 Icelandic Stock 9 5 Icelandic Stock 5 Icelandic Stock 2 Icelandic Stock 4 Table 5.6: The Icelandic stocks divided into ﬁve risk categories. 64 Managing Settlement Risk in Banking

5.4 Probability of the Exchange Rate of a Currency Cross at Time T Being Less than at Time t Plus Cost

The objective in this section is to calculate the probability that the exchange rate of a currency cross at time T is less than at time t plus the cost (0.75%) for foreign exchange forward contracts. The probabilities were calculated for the currency crosses mentioned in earlier chapters by using equation 4.22. However, some assumptions had to be made in order to calculate the probabilities. For instance, the contract dates were missing. Therefore the lifetimes of the foreign exchange forward contracts had to be assumed and were assigned random lifetimes ranging from 4-12 months. The bank is always in the same position to the FX forward contracts. If we take the currency cross DKK/ISK as an example. The bank is agreeing to receive Danish Krones (DKK) in exchange for Icelandic Krones (ISK) at time T, on the already agreed upon exchange rate X(t). An example of how an increase/decrease in the exchange rate X(T ) in FX forward contracts affects the bank can be seen in table 5.7. If the exchange rate increases at time T to X(T ) = 15.5 it would mean that the bank would receive 200 DKK in exchange for 3000 ISK (X(t) = 15) but could sell the 200 DKK again and take a proﬁt of 3100-3000 = 100 ISK. If the exchange rate decreases the bank would similarly lose 3000-2900 = 100.

Time X(time) Amount (DKK) Amount (ISK) t 15 200 3000 Rate Increases T 15.5 200 3100 Rate Decreases T 14.5 200 2900

Table 5.7: An example of how an increase/decrease in the exchange rate X(T ) in FX forward contracts affects the bank.

However, let us now imagine that the counterparty would fail to settle and the bank were exposed to default/settlement risk. If the bank needed the 200 DKK he would have to exchange at the future exchange rate, T. If the exchange rate increases to X(T ) = 15.5 the bank needs to pay 3100 for 200 DKK. If the exchange rate decreases to X(T ) = 14.5 the bank would pay less for 200 DKK or 2900 ISK. To sum it up. If the counterparty would comply with the contract it would be more favorable for the bank if the exchange rate increased. However, if the counterparty would fail to settle leaving the bank exposed to default/settlement risk it would favor the bank more if the exchange rate decreased and that the probability of X(T ) X(t)(1 + c ) was high.  r Þórdís Sara Ársælsdóttir 65

A histogram of the probability of X(T ) X(t)(1 + c ) depending on the underlying  r currency cross can be seen in ﬁgure 5.20.

Figure 5.20: A histogram of the probability of X(T ) X(t)(1+c ) for foreign exchange  r forwards and the underlying currency crosses.

If a counterparty would default/fail to settle the currency crosses on the right hand side of graph 5.20 are more favorable. Currency crosses such as:

ISK/EUR • ISK/SEK • ISK/DKK • ISK/USD • ISK/NOK • ISK/GBP • where the bank is receiving Icelandic Krona in exchange for foreign currency all have 0.5 probabilities. Other currency crosses such as GBP/USD, EUR/NOK, USD/ISK, GBP/ISK, NOK/ISK and SEK/ISK range from 25% to 50% probability of the exchange rate decreasing at time T. 66 Managing Settlement Risk in Banking

As with the equity forwards, the bank could divide the underlying FX forwards into risk categories. The division of risk categories for FX forwards is not as straightforward as for the equity forwards. However the division could look something like in table5.8.

Category Currency Cross 1 ISK/EUR ISK/DKK 2 ISK/SEK ISK/USD ISK/NOK ISK/GBP 3 GBP/USD EUR/NOK 4 USD/ISK GBP/ISK 5 NOK/ISK SEK/ISK 6 EUR/ISK DKK/ISK Table 5.8: The underlying currency crosses in FX forwards divided into ﬁve risk categories.

Risk category one is the least risky and category six is the most risky. The bank could take an extra fee for the added risk of doing FX forward contracts with the higher risk counterparties based on the underlying currency cross’s risk category. 67

Chapter 6

Conclusion

6.1 Recommendations for the Bank

The conclusions and recommendations of this thesis should be useful for the bank. If we go back to the statistics chapter for the shares, bonds and funds it is clear the bank would beneﬁt from minimizing the settlement times. The bank is settling a fair amount of contracts with settlement times ranging from T+4 to T+7. Another preventative action the bank can take is to request cash from counterparties before going on exchange and purchasing the shares, funds and bonds. However, as stated by an employee of the bank, the bank cannot request this by all counterparties. The bank wouldn’t be able to compete with others on the market if it would request this by the large counterparties. Large counterparties could be simultaneously selling an asset elsewhere and buying another asset from the bank. Some counterparties simply do not have the cash available on the transaction date.

The probability of S(T ) S(t)+cost for the stocks and funds is volatile. In most cases  the stock/fund either got a probability really close to 100% or 0%. The reason for that is most likely due to the short settlement times, ranging from 0-21 days. However, the bank could use the probability methods to quantify the probability of loss if exposed to settlement risk, and take a fee from these higher risk customers accordingly. For example, if a fairly unknown customer/counterparty asks to purchase shares in a stock. After estimat- ing with the drift µ and volatility of the stock, using the expected settlement time, price of the stock and fees, the bank could calculate the probability of failure for that customer. If the calculations would tell the bank that the probability of S(T ) S(t)+cost was  high for that speciﬁc trade the bank could request an extra fee for the extra risk it would 68 Managing Settlement Risk in Banking be taking.

My recommendation for the bank when it comes to equity forwards is to categorize the underlying stocks into risk categories based on the pattern of the data. In this thesis the categories are ﬁve for the data. So, the bank could take an extra fee for the added risk of doing equity forward contracts with these higher risk counterparties based on the underlying stock’s risk category.

The same recommendations as for the equity forwards apply for the foreign exchange forwards. The risk categories identiﬁed in this thesis range from 1-6. Risk category 1 being the least risky and category 6 being the most risky. The bank could take an extra fee for the added risk of entering into FX forward contracts with these higher risk counterparties based on the underlying currency cross’s risk category.

6.2 Limitations

The thesis came across some limitations which are listed below.

The lifetimes of the foreign exchange forwards had to be assumed and randomized. • A larger number of FX forward and FX spot contracts are missing transaction time • stamps. The ones who are missing the time stamps are also the ones thought to be likely to be exposed to settlement risk.

The difficulty in finding/collecting historical prices for all shares. • The bank does not use fixed interest rates such as Libor, Reibor and so forth. The • bank either uses forward rates on the market in the case of currency in exchange for another currency. Or they use their own "feed" on forward rates that are converted into other currencies.

6.3 Further Work

A suggestion for further work would be to quantify and come up with a method to measure the settlement risk of the currency interest rate and interest rate swaps. As well as to quantify and measure the settlement risk of put and call options when the bank starts Þórdís Sara Ársælsdóttir 69 doing those trades.

Further work would be to put up a system/model that measures the risk and prices the ﬁnancial instruments in question based on counterparty, amount traded, underlying asset and the methods used in the thesis to calculate the probabilities.

I would like to look at foreign exchange spot transactions between the bank and larger foreign counterparties. Those transactions are stored in other databases and need more time from me.

As stated in the earlier section the thesis came across some limitations. I would like to be able to retrieve the real data for the lifetimes of the contracts and the interest rates used by the bank and do the calculations again with the real data. 70 71

Bibliography

Bank for International Settlements. (2013). Supervisory guidance for managing risks associated with the settlement of foreign exchange transactions. Beier, N., Harreis, H., Poppensieker, T., Sojka, D., & Thaten, M. (2010). Getting to grips with counterparty risk. McKinsey Working Papers on Risk, Number 20. Borio, C., McCauley, R., Turner, P., Cecchetti, S., Packer, F., Bergh, P., . . . Remolona, E. (2008). International banking and financial market developments (report). Chatterjee, S. (2015). Modelling credit risk. Centre for Central Banking Studies, 1-29. Chin, E., Nel, D., & Ólafsson, S. (2014). Problems and solutions in mathematical finance (Vol. 1). Wiley. Chin, E., Nel, D., & Ólafsson, S. (2017). Problems and solutions in mathematical finance (Vol. 2). Wiley. Deutche Bank. (2016). Pillar 3 report 2016. E. I. Altman, A. S. (1998). Credit risk measurement: Developments over the last 20 years. Handelsbanken. (2016). Risk and capital management, pillar 3. Hull, J. C. (2012). Options, futures and other derivatives. Pearson. Jyske Bank. (2016). Risk and capital management, pillar 3. Nordea. (2016). Capital and risk management report 2016, pillar 3. SEB. (2016). Capital adequacy and risk management report, pillar 3. Swedbank. (2015). Risk management and capital adequacy report. Íslandsbanki. (2016). Pillar 3 report: Risk and capital management 20016 (report). Ólafsson, S. (2018). Introduction to forwards and futures. 72