信用風(fēng)險(xiǎn)模資料新型(-)課件

IssuesinCreditRiskModellingRiskManagementSymposiumSeptember2,2000BankofThailandChotibhakJotikasthira1OverviewBISregulatorymodelVsCreditriskmodelsCurrentIssuesinCreditRiskModellingBriefintroductiontocreditriskmodelsPurposeofacreditriskmodelCommoncomponentsModelfrominsurance(CreditRisk+)CreditMetricsKMVModelcomparisonBankofThailand2RiskManagementSymposium-September2000BISRegulatoryModelVsCreditRiskModelsBISRisk-BasedCapitalRequirements

Allprivate-sectorloans(uncollateralized)aresubjectedtoan8percentcapitalreserverequirement,irrespectiveofthesizeoftheloan,itsmaturity,andthecreditqualityoftheborrowingcounterparty.

Note:Someadjustmentsaremadetocollateralized/guaranteedloanstoOECDgovernments,banks,andsecuritiesdealers.BankofThailand3RiskManagementSymposium-September2000CreditRiskModels -CreditRisk+ -CreditMetrics -KMV -OthersimilarmodelsBISRegulatoryModelVsCreditRiskModelsBankofThailand4RiskManagementSymposium-September2000DisadvantagesofBISRegulatoryModel1.Doesnotcapturecredit-qualitydifferencesamongprivate-sectorborrowers2.IgnoresthepotentialforcreditriskreductionvialoandiversificationThesepotentiallyresultintoolargeacapitalrequirement!!!!!

BISRegulatoryModelVsCreditRiskModelsBankofThailand5RiskManagementSymposium-September2000BISRegulatoryModelVsCreditRiskModelsBigdifferenceinprobabilityofdefaultexistsacrossdifferentcreditqualities.

Note:1.Probabilityofdefaultisbasedon1-yearhorizon.2.HistoricalstatisticsfromStandard&Poor’sCreditWeekApril15,1996.BankofThailand6RiskManagementSymposium-September2000BISRegulatoryModelVsCreditRiskModels

Defaultcorrelationscanhavesignificantimpactonportfoliopotentialloss.KMVfindsthatcorrelationstypicallylieintherange0.002to0.15.

8%8%BISmodelrequires8%oftotal.8%8%Correlation=1Correlation=0.15Actualexposureisonly6%oftotal.BankofThailand7RiskManagementSymposium-September2000BISRegulatoryModelVsCreditRiskModels

Thecapitalrequirementtocoverunexpectedlossdecreasesrapidlyasthenumberofcounterpartiesbecomeslarger.

Unexpectedloss#ofcounterparties1168%3.54%Assumption:Allloansareofequalsize,andcorrelationsbetweendifferentcounterpartiesare0.15.BankofThailand8RiskManagementSymposium-September2000CurrentIssuesinCreditRiskModellingAdaptedfrom“CreditRiskModelling:CurrentPracticesandApplications”,April1999,byBasleCommitteeonBankingSupervisionBankofThailand9RiskManagementSymposium-September2000CurrentIssuesinCreditRiskModellingAdaptedfrom“CreditRiskModelling:CurrentPracticesandApplications”,April1999,byBasleCommitteeonBankingSupervisionBankofThailand10RiskManagementSymposium-September2000CurrentIssuesinCreditRiskModellingAdaptedfrom“CreditRiskModelling:CurrentPracticesandApplications”,April1999,byBasleCommitteeonBankingSupervisionBankofThailand11RiskManagementSymposium-September2000CurrentIssuesinCreditRiskModellingAdaptedfrom“CreditRiskModelling:CurrentPracticesandApplications”,April1999,byBasleCommitteeonBankingSupervisionBankofThailand12RiskManagementSymposium-September2000CreditRiskModels(A)PurposeofacreditriskmodelMeasuringeconomicriskcausedbyDefaultsDownratingsIdentifyingrisksourcesandtheircontributionsScenarioanalysisandStresstestEconomiccapitalrequirementandallocationPerformanceevaluation(e.g.RAROC)BankofThailand13RiskManagementSymposium-September2000CreditRiskModels(B)CommonComponents

1.ModelstructureTransaction1Transaction2...Transaction1Transaction2...CounterpartyACounterpartyB……PortfolioofseveralcounterpartiesandtransactionsCorrelationsBankofThailand14RiskManagementSymposium-September2000CreditRiskModels2.Quantitativevariables/parameters

-Defaultprobability/intensity(PD,EDF) -Loanequivalentexposure(LEE) -Lossgivendefault(LGD),Recoveryrate(RR),Severity(SEV) -Lossdistribution -Expectedloss(EL) -Unexpectedloss(UL),Portfoliorisk -Economiccapital(EC) -Riskcontributions(RC),Contributoryeconomiccapital(CEC)BankofThailand15RiskManagementSymposium-September2000CreditRiskModels(C)ModelfromInsurance(CreditRisk+) -Onlytwostatesoftheworldareconsidered-defaultandnodefault. -Spreadchanges(bothduetomarketmovementandratingupgrades/downgrades)areconsideredpartofmarketrisk. -Defaultprobabilityismodeledasacontinuousvariable.

BankofThailand16RiskManagementSymposium-September2000CreditRiskModels(C)ModelfromInsurance(CreditRisk+) Thereare3typesofuncertainty: 1.Actualnumberofdefaultsgivenameandefaultintensity 2.Meandefaultintensity(onlyinthenewapproach!) 3.Severityofloss

BankofThailand17RiskManagementSymposium-September2000CreditRiskModels(C)ModelfromInsurance(CreditRisk+) Thewholeloanportfoliocanbedividedintoclasses,eachofwhichconsistsofborrowerswithsimilardefaultrisk.Hence,aportfolioofloanstoeachclassofborrowerscanbeviewedasauniformportfolio.

-mcounterparties -auniformdefaultprobabilityofp(m)BankofThailand18RiskManagementSymposium-September2000CreditRiskModels(C)ModelfromInsurance(CreditRisk+)

DPCounterpartiesm1,p(m1)m2,p(m2)m3,p(m3)m4,p(m4)BankofThailand19RiskManagementSymposium-September2000CreditRiskModels(C)ModelfromInsurance(CreditRisk+) Withineachclassofcounterparties,numberofdefaultsfollowsPoissonDistribution.m=numberofcounterpartiesp(m)=uniformdefaultprobabilityn=numberofdefaultsin1yearBankofThailand20RiskManagementSymposium-September2000CreditRiskModels(C)ModelfromInsurance(CreditRisk+) Ifdefaultintensity()isconstant,defaultsareimplicitlyassumedtobeindependent(zerocorrelation).Thisistheoldapproach. Weknowthatcounterpartiesaresomewhatdependent.Asaresult,theoldapproachisnotrealistic(toooptimistic).BankofThailand21RiskManagementSymposium-September2000CreditRiskModels(C)ModelfromInsurance(CreditRisk+) Thenewapproachincorporatesdependencyofcounterpartiesbyassumingthatdefaultintensityisrandomandfollowsgammadistribution.

definesshape,anddefinesscaleofthedistribution.DefaultintensityProbabilitydensityBankofThailand22RiskManagementSymposium-September2000CreditRiskModels(C)ModelfromInsurance(CreditRisk+)

Numberofdefaults(n)Defaultintensity(

)BankofThailand23RiskManagementSymposium-September2000CreditRiskModels(C)ModelfromInsurance(CreditRisk+) Defaultsarenowrelatedsincetheyareexposedtothesamedefaultintensity.Higherdefaultintensityeffectsallobligorsintheportfolio.Firstmoment:Secondmoment:Mean>Variance(Over-dispersion)BankofThailand24RiskManagementSymposium-September2000CreditRiskModels(C)ModelfromInsurance(CreditRisk+) NegativeBinomialDistribution(NGD)exhibitsover-dispersionand“fattertails”,whichmakeitclosertorealitythanPoissonDistribution.#ofdefaultsProbabilitydensityPoissonNegativeBinomialEL(P)=EL(NGD)UL(P)<UL(NGD)BankofThailand25RiskManagementSymposium-September2000CreditRiskModels(C)ModelfromInsurance(CreditRisk+) Thelastsourceofuncertaintyisthelossamountincaseofdefault(LEE*LGD) Thisismodeledbybucketingintoexposurebandsandidentifyingtheprobabilitythatadefaultedobligorhasalossinagivenbandwiththepercentageofallcounterpartieswithinthisgivenband.BankofThailand26RiskManagementSymposium-September2000CreditRiskModels(C)ModelfromInsurance(CreditRisk+)

ProbabilityDistributionofLossAmountBankofThailand27RiskManagementSymposium-September2000CreditRiskModels(C)ModelfromInsurance(CreditRisk+)

Probabilitydistributionof#ofdefaultsProbabilitydistributionoflossamountTheanalyticformulaofthelossdistributionintheformofprobabilitygeneratingfunction(PGF)Probability,EL,UL,andPercentilecanbefound.BankofThailand28RiskManagementSymposium-September2000CreditRiskModels(D)CreditMetrics -Introducedin1997byJ.P.Morgan. -Bothdefaultsandspreadchangesduetoratingupgrades/downgradesareincorporated. -Creditmigration(includingdefault)isdiscrete. -Allcounterpartieswiththesamecreditratinghavethesameprobabilityofratingupgrades,ratingdowngrades,anddefaults.BankofThailand29RiskManagementSymposium-September2000CreditRiskModels(D)CreditMetrics Analysisisdoneoneachindividualcounterparty,whichwillthenbecombinedintoaportfolio,usingcorrelations.Therefore,theonlykeytypeofuncertaintymodeledhereisthecreditrating(ordefault)atwhichaparticularcounterpartywillbeoneyearfromnow.BankofThailand30RiskManagementSymposium-September2000CreditRiskModels(D)CreditMetrics

RatingTime01BBBBBBAAABDefaultBankofThailand31RiskManagementSymposium-September2000CreditRiskModels(D)CreditMetrics Inthecounterpartylevel,twoinputsarerequired: 1.Credittransitionmatrix(Moody’s,S&PorKMV)Source:Standard&Poor’sCreditWeekApril15,1996BankofThailand32RiskManagementSymposium-September2000CreditRiskModels(D)CreditMetrics 2.SpreadmatrixandrecoveryratesSource:Carty&Lieberman(96a)-Moody’sInvestorServiceBankofThailand33RiskManagementSymposium-September2000CreditRiskModels(D)CreditMetrics Possiblevaluesofloanoneyearfromnowcanthenbecalculated,eachofwhichhasitsownprobability:Now,theloanisratedBBB.ItsbondequivalentyieldisRf+SBBB.1yearBankofThailand34RiskManagementSymposium-September2000CreditRiskModels(D)CreditMetricsLoss=Vcurrent-VnewEL,UL,Percentile,andVaRcanbefound.E(V)V(1st-percentile)VaRBankofThailand35RiskManagementSymposium-September2000CreditRiskModels(D)CreditMetrics

Intheportfoliolevel,correlationsareneededtocombineallcounterparties(orloans)andfindtheportfoliolossdistribution: -“Abilitytopay”=“Normalizedequityvalue” -Migrationprobabilitiespredefinebuckets(lowerandupperthresholds)forthefutureabilitytopay -Correlationofdefaultandmigrationscan,hence,bederivedfromcorrelationofthe“abilitytopay”.BankofThailand36RiskManagementSymposium-September2000CreditRiskModels(D)CreditMetrics Inordertofindthelossdistributionofa2-counterpartyportfolio,weneedtocalculatethejointmigrationprobabilitiesandthepayoffsforeachpossiblescenario:Probabilitythatcounterparty1and2willberatedBBandBBBrespectivelyBankofThailand37RiskManagementSymposium-September2000CreditRiskModels(D)CreditMetricsSampleJointTransitionMatrix(assuming0.3assetcorrelation)Source:CreditMetrics-TechnicalDocument,April2,1997,p.38BankofThailand38RiskManagementSymposium-September2000CreditRiskModels(D)CreditMetrics

ForNcounterparties,onewaytofindthelossdistributionistokeepexpandingthejointtransitionmatrix.This,however,rapidlybecomescomputationallydifficult(thenumberofpossiblejointtransitionprobabilitiesis8N). Anotherwayistosumcounterpartyassetvolatilitiesistousethevariancesummationequation.Thisisacceptableonlyforthelossdistributionsthatareclosetonormal.BankofThailand39RiskManagementSymposium-September2000CreditRiskModels(D)CreditMetrics

Forcomputingthedistributionofloanvaluesinthelargesamplecasewhereloanvaluesarenotnormallydistributed,CreditMetricsusesMonteCarlosimulation. TheCreditMetricsportfoliomethodologycanalsobeusedforcalculatingthemarginalriskcontribution(RC)forindividualcounterparties.RCisusefulinidentifyingthecounterpartiestowhichwehaveexcessiveriskexposure.BankofThailand40RiskManagementSymposium-September2000CreditRiskModels(D)CreditMetrics

ExposureDistributionRatingmigrationlikelihoodsSpreadmatrixandrecoveryratesCorrelationsJointcreditratingchangesPortfoliocomponentsandmarketvolatilitiesValueandlossdistributionofindividualobligorsPortfoliovalueandlossdistributionEL,UL,Percentile,andVaRcanbefound.SummaryBankofThailand41RiskManagementSymposium-September2000CreditRiskModels(E)“KMV-Type”Model -Oneorbothdefaultsandspreadchangesduetoratingupgrades/downgradescanbeincorporated. -EDFisfirm-specific. -EDFvariescontinuouslywithfirmassetvalueandvolatility. -Potentiallyacontinuouscreditmigration.BankofThailand42RiskManagementSymposium-September2000CreditRiskModels(E)“KMV-Type”Model Analysisisdoneoneachindividualcounterparty,whichwillthenbecombinedintoaportfolio,usingasset-valuecorrelations.Therefore,theonlykeytypeofuncertaintymodeledhereiswhetherornottheassetvalueofeachfirm,oneyearfromnow,willbehigherthanthevalueofitsliabilities.BankofThailand43RiskManagementSymposium-September2000CreditRiskModels(E)“KMV-Type”ModelAbilitytopay=AssetvalueTime01Defaultpoint=ValueofliabilitiesAssetvaluedistributionDefaultprobabilityValueBankofThailand44RiskManagementSymposium-September2000CreditRiskModels(E)“KMV-Type”Model Thequestionis“howtofindthedistributionoffutureassetvalue”. KMVdefinesthedistributionbythemeanassetvalueandtheassetvolatility(orstandarddeviation).Thequestionnowbecomes“howtofindtheassetvalueanditsvolatility”.BankofThailand45RiskManagementSymposium-September2000CreditRiskModels(E)“KMV-Type”Model Sincewecanobserveonlyequityvalueanditsvolatility,thelinkbetweenequityandassetvaluesandthatbetweenequityandassetvolatilitiesneedtobeestablished.KMVsolvethisproblemusinganoptionpricingmodel.BankofThailand46RiskManagementSymposium-September2000CreditRiskModels(E)“KMV-Type”Model0FirmvalueLiabilityvalue0FirmvalueEquityvalueBookvalueofliabilitiesBookvalueofliabilitiesLiabilities~“Shortput”Equity~“Longcall”BankofThailand47RiskManagementSymposium-September2000CreditRiskModels(E)“KMV-Type”Model Equityislikeacalloptiononthefirmasset:Twounknowns(and)canbesolvedfromthesetwoequations.BankofThailand48RiskManagementSymposium-September2000CreditRiskModels(E)“KMV-Type”Model Distancetodefault(DD)isthencalculated:Sincetheassetvaluedistributionisnotnormal,KMVlinksDDtoEDFusinghistoricalrelationship.BankofThailand49RiskManagementSymposium-September2000CreditRiskModels(E)“KMV-Type”Model KMVclaimsthatforagivenDD,EDFisremarkablyconstantacrosskeyvariables: -Industry/sector -Companysize -Time ThisprovidesarobustbasisforDD-EDFmapping.BankofThailand50RiskManagementSymposium-September2000CreditRiskModels(E)“KMV-Type”Model

LikeCreditMetrics,correlationsareneededtocombineallcounterparties(orloans)intoaportfolioandfindtheportfoliolossdistribution: -“Abilitytopay”=“Marketvalueofthefirmasset” -EDFisdefinedasachancethatthe“abilitytopay”willreachthedefaultpoint. -Correlationofdefaultcan,hence,bederivedfromcorrelationofassetvalue.BankofThailand51RiskManagementSymposium-September2000CreditRiskModels(E)“KMV-Type”Model

For2counterparties,thejointdefaultprobabilitycanbecalculatedasfollows: Foralargenumberofcounterparties,jointprobabilitiescouldbecomecomputationallydifficult(thenumberofjointprobabilitiesis2N).BankofThailand52RiskManagementSymposium-September2000CreditRiskModels(E)“KMV-Typ