| Validation of Risk Management Models for Financial Institutions Financial models are an inescapable feature of modern financial markets. Yet, it was over-reliance on these models and the failure to test them properly that is now widely recognized as one of the main causes of the financialcrisisof2007–2011.Sincethiscrisis,therehasbeenanincreasein theamountofscrutinyandtestingappliedtosuchmodels,andvalidation hasbecomeanessentialpartofmodelriskmanagementatfinancialinsti- tutions.Thebookcoversallthemajorriskareasthatafinancialinstitution isexposedtoandusesmodelsfor,includingmarketrisk,interestraterisk, retail credit risk, wholesale credit risk, compliance risk and investment management.Thebookdiscussescurrentpracticesandpitfallsthatmodel riskusersneedtobeawareofanditidentifiesareaswherevalidationcan be advanced in the future. This provides the first unified framework for validatingriskmanagementmodels. david lynch is Deputy Associate Director for Policy Research and Analytics at the Board of Governors of the Federal Reserve System. He joined the board in 2005, and his areas of responsibility include Volcker metrics,swapmargin,andoversightofmodelsformarketriskcapitaland counterpartyriskcapital. iftekharhasanisUniversityProfessorandE.GeraldCorriganChairin FinanceatFordhamUniversity.HeistheeditoroftheJournalofFinancial Stabilityandisamongthemostwidelycitedacademicsintheworld. Akhtar Siddique taught finance at Georgetown University after his financePh.D.atDukeUniversity.Hehaspublishedextensivelyinleading financejournalsandcurrentlyworksattheOfficeoftheComptrollerofthe Currency. Validation of Risk Management Models for Financial Institutions Theory and Practice Edited by david lynch FederalReserveBoardofGovernors iftekhar hasan FordhamUniversityGraduateSchoolsofBusiness akhtar siddique OfficeoftheComptrolleroftheCurrency ShaftesburyRoad,CambridgeCB28EA,UnitedKingdom OneLibertyPlaza,20thFloor,NewYork,NY10006,USA 477WilliamstownRoad,PortMelbourne,VIC3207,Australia 314–321,3rdFloor,Plot3,SplendorForum,JasolaDistrictCentre, NewDelhi–110025,India 103PenangRoad,#05–06/07,VisioncrestCommercial,Singapore238467 CambridgeUniversityPressispartofCambridgeUniversityPress&Assessment,a departmentoftheUniversityofCambridge. WesharetheUniversity’smissiontocontributetosocietythroughthepursuitof education,learningandresearchatthehighestinternationallevelsofexcellence. www.cambridge.org Informationonthistitle:www.cambridge.org/9781108497350 DOI:10.1017/9781108608602 ©CambridgeUniversityPress&Assessment2023 Thispublicationisincopyright.Subjecttostatutoryexceptionandtotheprovisions ofrelevantcollectivelicensingagreements,noreproductionofanypartmaytake placewithoutthewrittenpermissionofCambridgeUniversityPress&Assessment. Firstpublished2023 AcataloguerecordforthispublicationisavailablefromtheBritishLibrary. LibraryofCongressCataloging-in-PublicationData Names:Lynch,David,1964–editor.|HasanIftekhar,editor.|Siddique,AkhtarR.,editor. Title:Validationofriskmanagementmodelsforfinancialinstitutions:theoryand practice/editedbyDavidLynch,FederalReserveBoardofGovernors,IftekharHasan, FordhamUniversityGraduateSchoolsofBusiness,AkhtarSiddique,Officeofthe ComptrolleroftheCurrency. Description:Firstedition.|NewYork,NY:CambridgeUniversityPress,[2022]| Includesbibliographicalreferencesandindex. Identifiers:LCCN2022012256(print)|LCCN2022012257(ebook)|ISBN 9781108497350(hardback)|ISBN9781108739962(paperback)|ISBN 9781108608602(epub) Subjects:LCSH:Finance–Mathematicalmodels.|Financialinstitutions–Mathematical models.|Riskmanagement.|Quantitativeresearch–Evaluation. Classification:LCCHG106.V352022(print)|LCCHG106(ebook)|DDC332/.01/ 5118–dc23/eng/20220418 LCrecordavailableathttps://lccn.loc.gov/2022012256 LCebookrecordavailableathttps://lccn.loc.gov/2022012257 ISBN978-1-108-49735-0Hardback CambridgeUniversityPress&Assessmenthasnoresponsibilityforthepersistence oraccuracyofURLsforexternalorthird-partyinternetwebsitesreferredtointhis publicationanddoesnotguaranteethatanycontentonsuchwebsitesis,orwill remain,accurateorappropriate. Contents List of Figures pagevii List of Tables x List of Contributors xiii Foreword xv ChristopherFinger Acknowledgments xvii 1 Common Elements inValidation of Risk Models Used in Financial Institutions 1 David Lynch, Iftekhar Hasan and Akhtar Siddique 2 Validating Bank Holding Companies’Value-at-Risk Models for Market Risk 22 David Lynch 3 AConditional Testing Approach forValue-at-RiskModel Performance Evaluation 49 VictorK. Ng 4 Beyond Exceedance-Based Backtesting of Value-at-Risk Models: Methodsfor Backtesting the Entire Forecasting Distribution UsingProbability IntegralTransform 57 Diana Iercosan,Alysa Shcherbakova, David McArthur and Rebecca Alper 5 Evaluation of Value-at-Risk Models: AnEmpirical Likelihood Approach 84 David Lynch, Valerio Potì, AkhtarSiddiqueand Francesco Campobasso 6 Evaluating Banks’Value-at-RiskModels during the COVID-19 Crisis 104 ChrisAnderson and Dennis Mawhirter v vi Contents 7 Performance Monitoring for SupervisoryStress- Testing Models 124 Nick Klagge and Jose A. Lopez 8 Counterparty Credit Risk 156 Eduardo Canabarro 9 Validation of Retail Credit RiskModels 175 Sang-Sub Lee and Feng Li 10 Issues in theValidation of Wholesale Credit Risk Models 232 Jonathan Jones and Debashish Sarkar 11 Case Studies in Wholesale Risk Model Validation 263 DebashishSarkar 12 Validation ofModels Used by Banks to Estimate Their Allowance forLoan and Lease Losses 295 Partha Sengupta 13 Operational Risk 331 Filippo Curti, Marco Migueis and Robert Stewart 14 StatisticalDecisioning Toolsfor Model Risk Management 359 Bhojnarine R. Rambharat 15 Validation ofRiskAggregation inEconomic Capital Models 379 Ibrahim Ergen,HulusiInanogluand David Lynch 16 Model Validationof InterestRate Risk (Banking Book) Models 422 Ashish Dev 17 Validation ofRiskManagement Models in InvestmentManagement 439 Akhtar Siddique Index 445 Figures 4.1a Totalexceedancesbysubportfolio(winzorized). page62 4.1b Top of the house exceedancesby bank (winzorized). 62 4.2a PIT distribution. 63 4.2b Top of the house PIT distribution. 63 4.3a CDF of PIT distribution. 64 4.3b Top of the house CDF of PIT distribution. 64 4.4a Subportfolio moments ofthedistribution of PITs. 66 4.4b Top of the house momentsof the distribution of PITs. 67 4.5 PITs vs lagged PITs. 81 6.1 Percent of desks with backtesting exceptions over time. 108 7.1 Scenario sensitivity testing using scatterplots. 135 7.2 Model’s scenario sensitivity with reference toa macroeconomic variable. 137 7.3 Scenario sensitivity across multiple portfolio segments and a macroeconomic variable. 138 7.4 Scenario sensitivity testing using scatterplotsof stock return projections. 140 7.5 Scenario sensitivity across industry sectors and scenario index returns. 141 7.6 Benchmarking analysis of theCAPMand naïve models across scenarios. 147 8.1 Market values and credit exposures, netted and non- netted. 158 8.2 EE and PE for a10-year interest rate swap without t t margin agreement. 160 vii viii ListofFigures 8.3 EE and PE fora 10-year cross-currency swap with t t finalexchangeof notional amountsand without margin agreement. 161 8.4 PE fora10-yearinterestrateswapwithandwithout t margin agreement. 162 8.5 PE for a 10-year cross-currency swap with final t exchange ofnotional amounts, with and without margin agreement. 162 8.6 Expected Exposurecreated by the portfolioof derivatives with counterpartyB. 163 8.7 Conditional expected exposure and marginalloss rates forthe portfolioof derivatives with counterpartyB. 163 8.8 CVA hedging profit and loss (P&L)undernormal market conditions and zero transaction costs. 171 8.9 CVA hedging profit and loss (P&L)undernormal market conditions and 5% transaction costs. 172 8.10 CVAhedging profit and loss (P&L) under stressed marketconditions and 5% transaction costs. 173 9.1 Householddebtto net disposableincomeby country2021. 176 9.2 Loans and liabilities ofUS household and nonprofits. 178 9.3 US Commercialbanksconsumer credit charge- offs. 178 9.4 Standardparametric models and their hazard and survivalfunctions. 190 9.5 Illustration of exploded panel. 196 9.6 Illustration of aretailtransition matrix for mortgage loans. 198 12.1 Conditional claims rates over differenthorizonsfor the2000, 2005 and 2010 loan charts. 303 12.2 Timeseriesof monthlyunemploymentrates, 1990–2016. 308 12.3 Conditional claims rates over differenthorizonsfor the2000, 2005 and 2010 loan charts (30-year fixed mortgages). 309 12.4 Illustration of payments on a credit card and allowance. 310