onls oeatn:amtoooia overview methodological a forecasting: loss Loan dadGffe,Rbr el,Pu yn,Fra McCann Fergal Lyons, Paul Kelly, Robert Gaffney, Edward a.cancnrlaki.Tevespeetdi hsppraetoeo h uhr ln n ontrepresent not do and own. alone our are authors errors remaining the Any . of Central those of System are European the paper or Ireland this of in Central the presented of views views official The the banks domestic [email protected]. the from collec- data the loan-level to due of possible tion made was manner rent completed recently Assessment. the Comprehensive to ECB/SSM akin losses assess- such of loan-level of Bank a ment undertaking Central of the capable at Ireland developed framework a pol- of prudential This a of framework. component icy core a is un- impor- and paramount tance evolve of is scenarios they macro current various how need quantify der and to the ability requirements in The provision rise resulting support. rapidly downturn state for can economic impairments an loan ex- in how acute an of is ample experience crisis financial Ireland’s Introduction 1 mortgage between choice lenders’ models repossession. which and algorithm internally-developed modification an using ( models mortgage Default residential Given Loss balance. internally- and includes banks, Irish domestic ( by basis six-monthly D P ( a default on of provided probability data developed loan-level detailed utilises which This EAD 1 h eeomn ftemdl ntercur- their in models the of development The mi:ewr.anycnrlaki,[email protected] alloscnrlaki fer- & [email protected] [email protected], edward.gaff[email protected], email: oespoieetmtso h rbblt of probability the of estimates provide models Letter scluae na nulbssusing basis annual an on calculated is ) rvdsa vriwo h eta ako rln’ onLs oeatn rmwr.Ti framework, This framework. Forecasting Loss Loan Ireland’s of Bank Central the of overview an provides Letter rvdsa overview an provides D P LGD oesadacs o niewihpoue xetdls siae.The estimates. loss expected produces which engine flow cash a and models ) scluae sn onlvlclaea au aaadcnb dutdin adjusted be can and data value collateral loan-level using calculated is ) o 04 o 13 No. 2014, Vol D P Abstract transition siae n onlvlifraino em neetrate interest term, on information loan-level and estimates 1 lcRc ouin nJn 03t nuethat ensure to 2013 by June conducted in was Solutions process BlackRock validation framework, the external individual of an these completion of Upon each components. for methodologies elling ( Default of at Probability Exposure of ( product the Default where are The framework losses loss standard expected portfolios. a follow loan all corporate models Enter- and Medium (SME) and prise Small credit, consumer mort-gage, of residential suite for a models of (bottom-up) Together, development loan-level the losses. for allow loan inputs these explain macroeconomic best the that are in- inputs variables key key as other The used are puts. that information collateral loan borrower, and detailed provides (2011). data granular Programme This Measures Financial the under noadoto ondfut xouea Default at Exposure default. loan of out and into D P ,Ls ie eal ( Default Given Loss ), EAD ,wt eaaemod- separate with ), LGD

and ) EconomicLeerSe Gaffney et al., loan loss forecasting the models were fit for purpose and met industry PD coefficients from the above-mentioned models standards. feed directly into the cash flow engine, and allow Flexibility is an essential component of model for changes in macroeconomic scenarios to impact development, to allow the models accommodate each loan’s PD. The model allows for regionally- changes in the banking or policy landscape. One varying unemployment and house price shocks to example in this framework is the inclusion of a loss impact loans differently. adjustment algorithm in the Irish residential mort- The of Ireland LLF model is gage model. The algorithm adjusts LGD for the unique in having developed a tool to model banks’ possibility that banks will offer mortgage modifica- choice between loan modifications and reposses- tions rather than move to repossession of defaulted sion (Gaffney and Dunne, 2014). This allows for mortgages. This mechanism (Gaffney and Dunne, lower portfolio LGD relative to standard LGD 2014) lowers LGD relative to a standard calcula- models which rely solely on collateral values at re- tion based on collateral values and repossession. possession. This letter introduces the Central Bank of Ire- land loan loss forecasting framework. A full de- Figure1 visualises the evolution of a hypothet- scription of the methodology and its components ical performing loan in the LLF. Certain aspects can be accessed in the material cited in this Letter. are simplified in this illustration. For instance, the An overview of the model is provided in Section 2. probabilities of default (PD) and cure (PC) are Section 3 provides a short conclusion. fixed at 5 and 10 per cent, respectively. The red arrows in each case indicate that 5 per cent of pe- riod t’s performing balance will transition to the 2 Model Overview defaulted state at (t + 1), while 90 per cent of pe- riod t’s defaulted balance will remain in default at The Loan Loss Forecasting model (LLF) estimates (t+1). The green arrows indicate that 10 per cent expected annual cash flows at the loan level. Cash of the default balance at t will move to performing flows, in this context, include flows between per- at (t + 1), while 95 per cent of the period t per- forming and defaulted states, as well as repayments forming balance will remain performing at (t + 1). of principal and write-offs of and recoveries from Performing balances are then amortised at a rate defaulted balances. The model combines informa- of 2 per cent in this illustration. tion on each loan’s characteristics, the macroeco- Figure2 provides an illustration of how the LLF nomic scenario inputs, coefficients on transitions to uses the default flows in Figure1 to estimate ex- default and cure and information regarding collat- pected loss. At t = 1 in this hypothetical exam- eral to estimate LGD. The model in its totality is ple, e5,000 is expected to be in default. Based summarised in Gaffney, Kelly, and McCann(2014). on Irish and international empirical evidence, the (PD) is derived from time that elapses between default and liquidation models developed internally in the Central Bank is set to be two years in this model, which explains of Ireland. These models generate estimates of why cure flows are only possible for two years af- the probability of transitioning into and out of de- ter the default events at t = 1 and t = 2. The fault, rather than the probability of being in de- two green arrows with cure rates of 10 and 8 per fault, which is the standard approach to modelling cent indicate that the portion of the loan that de- losses where prediction of the stock of losses is the faulted at (t + 1) will be allowed to cure for two primary aim. These estimates are arrived at using years, and that the probability of cure will fall as a continuous time version of a transition matrix time elapses. Figure1 illustrates clearly the level approach (See Lando and Skodeberg(2002) and of detail built into the LLF: for an individual loan (Jackson, 2011)). The Republic of Ireland (ROI) beginning at t = 0, the model traces out the prob- and UK residential models are detailed in Kelly and abilistic component that defaults at t = 1, along O’Malley(2014) and McCann(2014), respectively. with the two periods of potential cures emanating The LLF cash flow engine joins up the sub from that default. Further, it traces the compo- components of annual transition probabilities, cash nent that defaults at t = 2, and the subsequent flows and LGD’s to generate expected losses. The related two years of cure flows.2 2In practice there will also be default flows at t = 3, with resultant cure flows at t = 4 and t = 5. These are omitted for ease of exposition.

2 Gaffney et al., loan loss forecasting

3 Conclusion Enterprise (SME) and corporate portfolios. The models utilise detailed loan-level data submitted by The Central Bank of Ireland has developed a de- Irish banks to estimate transition probabilities be- tailed framework for estimating expected credit tween performing and defaulted loan status. These losses. The methods outlined in this Letter and the models have acted and will continue to act as part papers cited herein have been applied to residen- of a suite of prudential tools available to the Cen- tial mortgage, consumer credit, Small and Medium tral Bank of Ireland.

References

Gaffney, E., and P. Dunne (2014): “Enhanced modelling of mortgage for loan-loss fore- casting,” Mimeo, Central Bank of Ireland.

Gaffney, E., R. Kelly, and F. McCann (2014): “A transitions-based framework for estimating expected credit losses,” Research Technical Paper 16RT14, Central Bank of Ireland.

Jackson, C. (2011): “Multi-state models for panel data: The msm package for R,” Journal of Statistical Software, 38(8), 1–28.

Kelly, R., and T. O’Malley (2014): “A transitions-based model of default for Irish mortgages,” Research Technical Paper 17RT14, Central Bank of Ireland.

Lando, D., and T. M. Skodeberg (2002): “Analyzing rating transitions and rating drift with continuous observations,” Journal of Banking & Finance, 26(2-3), 423–444.

McCann, F. (2014): “Modelling default transitions in the UK mortgage market,” Research Technical Paper 18RT14, Central Bank of Ireland.

3 Gaffney et al., loan loss forecasting

Figures and Tables

Figure 1: Default and cure flows for 3-year horizon of a hypothetical performing loan

Time

0 1 2 3

PB = 100,000(1- PB = (93,100(1-PD) + PB = (87,166(1-PD) + PD)(1-AM) = (1-PD)=95% (5,000*PC)) * (1-AM) = (1-PD)=95% (9,155*PC)) * (1-AM) = 93,100 87,166 82,049 PD = 5% PD = 5% PB = 100,000 PC=10% PC=10% PD = 5%

DS = 100,000*PD DS = 5,000*(1-PC) + DS = 9,155*(1-PC) + = 5,000 (1-PC)=90% 93,100*PD = 9,155 (1-PC)=90% 87,166*PD – REPO= 8,547

Hypothetical loan with a t = 0 balance of e100,000, a constant set of parameters: PD of 5%, P Cure of 10% and an amortisation rate (AM) of 2%. PB refers to performing balance, DS to default stock in each year. PD and P Cure will vary at the loan level and will derive from the loan-level multi-state model’s coefficients. REPO at t = 2 refers to the e4,050 of t = 1 default stock that has not cured by t = 3, and is thus repossessed.

4 Gaffney et al., loan loss forecasting

Figure 2: Derivation of expected loss for portion of loan defaulting at t = 1 and t = 2

Time

0 1 2 3 4

DS1 = 100,000*PD PD = 5% = 5,000

PCt-2 = 8% PCt-1 = 10% PB = 100,000

Cure flows from loans CF = 5,000*PC = CF = (5,000- defaulting at t=1 500 500)*PC = 360

Lifetime Cures from loans LTC1=860 defaulting at t=1, LTC1

Exposure at Default from EAD1=(5,000-860) loans defaulting at t=1 = 4,140

Expected Loss from loans EL1=(4,140*50%) defaulting at t=1 = 2,070

DS1 =93,100*PD = PD = 5% 4,655 PD = 5%, AM=2%

PCt-2 = 8% PC = 10% PB = 93,100 t-1

Cure flows from loans CF = 4,655*PC = CF = (4,655- defaulting at t=2 466 465)*PC = 335

Lifetime Cures from loans LTC2=801 defaulting at t=2, LTC2

EAD =(4,655-801) from 2 = 3,854 loans defaulting at t=2

EL =(3,854*50%) Expected Loss from loans 2 = 1,927 defaulting at t=2

Hypothetical loan with a t = 0 balance of e100,000, and a constant set of parameters: PD of 5%; P Cure of 10% and 8% one year and two years after default, respectively, reflecting the negative impact of time in default in the model; LGD of 50%. PB refers to performing balance, DS refers to default stock. PD and P Cure will vary at the loan level and will derive from the loan-level multi-state model’s coefficients. PD does not vary over time in this example due to the simplifying assumption of an unchanging macroeconomic environment for the purposes of this display. 5