信用风险模型.ppt

IssuesinCreditRiskModelling,RiskManagementSymposiumSeptember2,2000,BankofThailand,ChotibhakJotikasthira,BankofThailand,RiskManagementSymposium-September2000,Page2,Overview,BISregulatorymodelVsCreditriskmodelsCurrentIssuesinCreditRiskModellingBriefintroductiontocreditriskmodelsPurposeofacreditriskmodelCommoncomponentsModelfrominsurance(CreditRisk+)CreditMetricsKMVModelcomparison,BankofThailand,RiskManagementSymposium-September2000,Page3,BISRegulatoryModelVsCreditRiskModels,BISRisk-BasedCapitalRequirementsAllprivate-sectorloans(uncollateralized)aresubjectedtoan8percentcapitalreserverequirement,irrespectiveofthesizeoftheloan,itsmaturity,andthecreditqualityoftheborrowingcounterparty.Note:Someadjustmentsaremadetocollateralized/guaranteedloanstoOECDgovernments,banks,andsecuritiesdealers.,BankofThailand,RiskManagementSymposium-September2000,Page4,CreditRiskModels-CreditRisk+-CreditMetrics-KMV-Othersimilarmodels,BISRegulatoryModelVsCreditRiskModels,BankofThailand,RiskManagementSymposium-September2000,Page5,DisadvantagesofBISRegulatoryModel1.Doesnotcapturecredit-qualitydifferencesamongprivate-sectorborrowers2.IgnoresthepotentialforcreditriskreductionvialoandiversificationThesepotentiallyresultintoolargeacapitalrequirement!,BISRegulatoryModelVsCreditRiskModels,BankofThailand,RiskManagementSymposium-September2000,Page6,BISRegulatoryModelVsCreditRiskModels,Bigdifferenceinprobabilityofdefaultexistsacrossdifferentcreditqualities.,Note:1.Probabilityofdefaultisbasedon1-yearhorizon.2.HistoricalstatisticsfromStandard&PoorsCreditWeekApril15,1996.,BankofThailand,RiskManagementSymposium-September2000,Page7,BISRegulatoryModelVsCreditRiskModels,Defaultcorrelationscanhavesignificantimpactonportfoliopotentialloss.KMVfindsthatcorrelationstypicallylieintherange0.002to0.15.,8%,8%,BISmodelrequires8%oftotal.,8%,Correlation=1,Correlation=0.15,Actualexposureisonly6%oftotal.,BankofThailand,RiskManagementSymposium-September2000,Page8,BISRegulatoryModelVsCreditRiskModels,Thecapitalrequirementtocoverunexpectedlossdecreasesrapidlyasthenumberofcounterpartiesbecomeslarger.,Unexpectedloss,#ofcounterparties,1,16,8%,3.54%,Assumption:Allloansareofequalsize,andcorrelationsbetweendifferentcounterpartiesare0.15.,BankofThailand,RiskManagementSymposium-September2000,Page9,CurrentIssuesinCreditRiskModelling,Adaptedfrom“CreditRiskModelling:CurrentPracticesandApplications”,April1999,byBasleCommitteeonBankingSupervision,BankofThailand,RiskManagementSymposium-September2000,Page10,CurrentIssuesinCreditRiskModelling,Adaptedfrom“CreditRiskModelling:CurrentPracticesandApplications”,April1999,byBasleCommitteeonBankingSupervision,BankofThailand,RiskManagementSymposium-September2000,Page11,CurrentIssuesinCreditRiskModelling,Adaptedfrom“CreditRiskModelling:CurrentPracticesandApplications”,April1999,byBasleCommitteeonBankingSupervision,BankofThailand,RiskManagementSymposium-September2000,Page12,CurrentIssuesinCreditRiskModelling,Adaptedfrom“CreditRiskModelling:CurrentPracticesandApplications”,April1999,byBasleCommitteeonBankingSupervision,BankofThailand,RiskManagementSymposium-September2000,Page13,CreditRiskModels,(A)PurposeofacreditriskmodelMeasuringeconomicriskcausedbyDefaultsDownratingsIdentifyingrisksourcesandtheircontributionsScenarioanalysisandStresstestEconomiccapitalrequirementandallocationPerformanceevaluation(e.g.RAROC),BankofThailand,RiskManagementSymposium-September2000,Page14,CreditRiskModels,(B)CommonComponents1.Modelstructure,Transaction1Transaction2.,Transaction1Transaction2.,CounterpartyA,CounterpartyB,Portfolioofseveralcounterpartiesandtransactions,Correlations,BankofThailand,RiskManagementSymposium-September2000,Page15,CreditRiskModels,2.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),BankofThailand,RiskManagementSymposium-September2000,Page16,CreditRiskModels,(C)ModelfromInsurance(CreditRisk+)-Onlytwostatesoftheworldareconsidered-defaultandnodefault.-Spreadchanges(bothduetomarketmovementandratingupgrades/downgrades)areconsideredpartofmarketrisk.-Defaultprobabilityismodeledasacontinuousvariable.,BankofThailand,RiskManagementSymposium-September2000,Page17,CreditRiskModels,(C)ModelfromInsurance(CreditRisk+)Thereare3typesofuncertainty:1.Actualnumberofdefaultsgivenameandefaultintensity2.Meandefaultintensity(onlyinthenewapproach!)3.Severityofloss,BankofThailand,RiskManagementSymposium-September2000,Page18,CreditRiskModels,(C)ModelfromInsurance(CreditRisk+)Thewholeloanportfoliocanbedividedintoclasses,eachofwhichconsistsofborrowerswithsimilardefaultrisk.Hence,aportfolioofloanstoeachclassofborrowerscanbeviewedasauniformportfolio.-mcounterparties-auniformdefaultprobabilityofp(m),BankofThailand,RiskManagementSymposium-September2000,Page19,CreditRiskModels,(C)ModelfromInsurance(CreditRisk+),BankofThailand,RiskManagementSymposium-September2000,Page20,CreditRiskModels,(C)ModelfromInsurance(CreditRisk+)Withineachclassofcounterparties,numberofdefaultsfollowsPoissonDistribution.,m=numberofcounterpartiesp(m)=uniformdefaultprobabilityn=numberofdefaultsin1year,BankofThailand,RiskManagementSymposium-September2000,Page21,CreditRiskModels,(C)ModelfromInsurance(CreditRisk+)Ifdefaultintensity()isconstant,defaultsareimplicitlyassumedtobeindependent(zerocorrelation).Thisistheoldapproach.Weknowthatcounterpartiesaresomewhatdependent.Asaresult,theoldapproachisnotrealistic(toooptimistic).,BankofThailand,RiskManagementSymposium-September2000,Page22,CreditRiskModels,(C)ModelfromInsurance(CreditRisk+)Thenewapproachincorporatesdependencyofcounterpartiesbyassumingthatdefaultintensityisrandomandfollowsgammadistribution.,definesshape,anddefinesscaleofthedistribution.,Defaultintensity,Probabilitydensity,BankofThailand,RiskManagementSymposium-September2000,Page23,CreditRiskModels,(C)ModelfromInsurance(CreditRisk+),Numberofdefaults(n),Defaultintensity(),BankofThailand,RiskManagementSymposium-September2000,Page24,CreditRiskModels,(C)ModelfromInsurance(CreditRisk+)Defaultsarenowrelatedsincetheyareexposedtothesamedefaultintensity.Higherdefaultintensityeffectsallobligorsintheportfolio.,Firstmoment:,Secondmoment:,MeanVariance(Over-dispersion),BankofThailand,RiskManagementSymposium-September2000,Page25,CreditRiskModels,(C)ModelfromInsurance(CreditRisk+)NegativeBinomialDistribution(NGD)exhibitsover-dispersionand“fattertails”,whichmakeitclosertorealitythanPoissonDistribution.,#ofdefaults,Probabilitydensity,EL(P)=EL(NGD)UL(P)UL(NGD),BankofThailand,RiskManagementSymposium-September2000,Page26,CreditRiskModels,(C)ModelfromInsurance(CreditRisk+)Thelastsourceofuncertaintyisthelossamountincaseofdefault(LEE*LGD)Thisismodeledbybucketingintoexposurebandsandidentifyingtheprobabilitythatadefaultedobligorhasalossinagivenbandwiththepercentageofallcounterpartieswithinthisgivenband.,BankofThailand,RiskManagementSymposium-September2000,Page27,CreditRiskModels,(C)ModelfromInsurance(CreditRisk+),ProbabilityDistributionofLossAmount,BankofThailand,RiskManagementSymposium-September2000,Page28,CreditRiskModels,(C)ModelfromInsurance(CreditRisk+),Probabilitydistributionof#ofdefaults,Probabilitydistributionoflossamount,Theanalyticformulaofthelossdistributionintheformofprobabilitygeneratingfunction(PGF),Probability,EL,UL,andPercentilecanbefound.,BankofThailand,RiskManagementSymposium-September2000,Page29,CreditRiskModels,(D)CreditMetrics-Introducedin1997byJ.P.Morgan.-Bothdefaultsandspreadchangesduetoratingupgrades/downgradesareincorporated.-Creditmigration(includingdefault)isdiscrete.-Allcounterpartieswiththesamecreditratinghavethesameprobabilityofratingupgrades,ratingdowngrades,anddefaults.,BankofThailand,RiskManagementSymposium-September2000,Page30,CreditRiskModels,(D)CreditMetricsAnalysisisdoneoneachindividualcounterparty,whichwillthenbecombinedintoaportfolio,usingcorrelations.Therefore,theonlykeytypeofuncertaintymodeledhereisthecreditrating(ordefault)atwhichaparticularcounterpartywillbeoneyearfromnow.,BankofThailand,RiskManagementSymposium-September2000,Page31,CreditRiskModels,(D)CreditMetrics,BankofThailand,RiskManagementSymposium-September2000,Page32,CreditRiskModels,(D)CreditMetricsInthecounterpartylevel,twoinputsarerequired:1.Credittransitionmatrix(Moodys,S&PorKMV),Source:Standard&PoorsCreditWeekApril15,1996,BankofThailand,RiskManagementSymposium-September2000,Page33,CreditRiskModels,(D)CreditMetrics2.Spreadmatrixandrecoveryrates,Source:Carty&Lieberman(96a)-MoodysInvestorService,BankofThailand,RiskManagementSymposium-September2000,Page34,CreditRiskModels,(D)CreditMetricsPossiblevaluesofloanoneyearfromnowcanthenbecalculated,eachofwhichhasitsownprobability:,Now,theloanisratedBBB.ItsbondequivalentyieldisRf+SBBB.,1year,BankofThailand,RiskManagementSymposium-September2000,Page35,CreditRiskModels,(D)CreditMetrics,Loss=Vcurrent-VnewEL,UL,Percentile,andVaRcanbefound.,E(V),V(1st-percentile),VaR,BankofThailand,RiskManagementSymposium-September2000,Page36,CreditRiskModels,(D)CreditMetricsIntheportfoliolevel,correlationsareneededtocombineallcounterparties(orloans)andfindtheportfoliolossdistribution:-“Abilitytopay”=“Normalizedequityvalue”-Migrationprobabilitiespredefinebuckets(lowerandupperthresholds)forthefutureabilitytopay-Correlationofdefaultandmigrationscan,hence,bederivedfromcorrelationofthe“abilitytopay”.,BankofThailand,RiskManagementSymposium-September2000,Page37,CreditRiskModels,(D)CreditMetricsInordertofindthelossdistributionofa2-counterpartyportfolio,weneedtocalculatethejointmigrationprobabilitiesandthepayoffsforeachpossiblescenario:,Probabilitythatcounterparty1and2willberatedBBandBBBrespectively,BankofThailand,RiskManagementSymposium-September2000,Page38,CreditRiskModels,(D)CreditMetrics,SampleJointTransitionMatrix(assuming0.3assetcorrelation),Source:CreditMetrics-TechnicalDocument,April2,1997,p.38,BankofThailand,RiskManagementSymposium-September2000,Page39,CreditRiskModels,(D)CreditMetricsForNcounterparties,onewaytofindthelossdistributionistokeepexpandingthejointtransitionmatrix.This,however,rapidlybecomescomputationallydifficult(thenumberofpossiblejointtransitionprobabilitiesis8N).Anotherwayistosumcounterpartyassetvolatilitiesistousethevariancesummationequation.Thisisacceptableonlyforthelossdistributionsthatareclosetonormal.,BankofThailand,RiskManagementSymposium-September2000,Page40,CreditRiskModels,(D)CreditMetricsForcomputingthedistributionofloanvaluesinthelargesamplecasewhereloanvaluesarenotnormallydistributed,CreditMetricsusesMonteCarlosimulation.TheCreditMetricsportfoliomethodologycanalsobeusedforcalculatingthemarginalriskcontribution(RC)forindividualcounterparties.RCisusefulinidentifyingthecounterpartiestowhichwehaveexcessiveriskexposure.,BankofThailand,RiskManagementSymposium-September2000,Page41,CreditRiskModels,(D)CreditMetrics,ExposureDistribution,Ratingmigrationlikelihoods,Spreadmatrixandrecoveryrates,Correlations,Jointcreditratingchanges,Portfoliocomponentsandmarketvolatilities,Valueandlossdistributionofindividualobligors,Portfoliovalueandlossdistribution,EL,UL,Percentile,andVaRcanbefound.,Summary,BankofThailand,RiskManagementSymposium-September2000,Page42,CreditRiskModels,(E)“KMV-Type”Model-Oneorbothdefaultsandspreadchangesduetoratingupgrades/downgradescanbeincorporated.-EDFisfirm-specific.-EDFvariescontinuouslywithfirmassetvalueandvolatility.-Potentiallyacontinuouscreditmigration.,BankofThailand,RiskManagementSymposium-September2000,Page43,CreditRiskModels,(E)“KMV-Type”ModelAnalysisisdoneoneachindividualcounterparty,whichwillthenbecombinedintoaportfolio,usingasset-valuecorrelations.Therefore,theonlykeytypeofuncertaintymodeledhereiswhetherornottheassetvalueofeachfirm,oneyearfromnow,willbehigherthanthevalueofitsliabilities.,BankofThailand,RiskManagementSymposium-September2000,Page44,CreditRiskModels,(E)“KMV-Type”Model,Abilitytopay=Assetvalue,Time,0,1,Defaultpoint=Valueofliabilities,Assetvaluedistribution,Defaultprobability,Value,BankofThailand,RiskManagementSymposium-September2000,Page45,CreditRiskModels,(E)“KMV-Type”ModelThequestionis“howtofindthedistributionoffutureassetvalue”.KMVdefinesthedistributionbythemeanassetvalueandtheassetvolatility(orstandarddeviation).Thequestionnowbecomes“howtofindtheassetvalueanditsvolatility”.,BankofThailand,RiskManagementSymposium-September2000,Page46,CreditRiskModels,(E)“KMV-Type”ModelSincewecanobserveonlyequityvalueanditsvolatility,thelinkbetweenequityandassetvaluesandthatbetweenequityandassetvolatilitiesneedtobeestablished.KMVsolvethisproblemusinganoptionpricingmodel.,BankofThailand,RiskManagementSymposium-September2000,Page47,CreditRiskModels,(E)“KMV-Type”Model,Firmvalue,Equityvalue,Bookvalueofliabilities,Bookvalueofliabilities,Liabilities“Shortput”,Equity“Longcall”,BankofThailand,RiskManagementSymposium-September2000,Page48,CreditRiskModels,(E)“KMV-Type”ModelEquityislikeacalloptiononthefirmasset:,Twounknowns(and)canbesolvedfromthesetwoequations.,BankofThailand,RiskManagementSymposium-September2000,Page49,CreditRiskModels,(E)“KMV-Type”ModelDistancetodefault(DD)isthencalculated:,Sincetheassetvaluedistributionisnotnormal,KMVlinksDDtoEDFusinghistoricalrelationship.,BankofThailand,RiskManagementSymposium-September2000,Page50,CreditRiskModels,(E)“KMV-Type”ModelKMVclaimsthatforagivenDD,EDFisremarkablyconstantacrosskeyvariables:-Industry/sector-Companysize-TimeThisprovidesarobustbasisforDD-EDFmapping.,BankofThailand,RiskManagementSymposium-September2000,Page51,CreditRiskModels,(E)“KMV-Type”ModelLikeCreditMetrics,correlationsareneededtocombineallcounterparties(orloans)intoaportfolioandfindtheportfoliolossdistribution:-“Abilitytopay”=“Marketvalueofthefirmasset”-EDFisdefinedasachancethatthe“abilitytopay”willreachthedefaultpoint.-Correlationofdefaultcan,hence,bederivedfromcorrelationofassetvalue.,BankofThailand,RiskManagementSymposium-September2000,Page52,CreditRiskModels,(E)“KMV-Type”ModelFor2counterpart