资源描述
Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Bank of Thailand,Risk Management Symposium - September 2000,Page,*,Issues in CreditRisk Modelling,RiskManagementSymposium,September 2,2000,BankofThailand,Chotibhak Jotikasthira,1,Overview,BISregulatory modelVsCredit riskmodels,CurrentIssues in CreditRisk Modelling,Brief introduction to creditrisk models,Purposeof acreditriskmodel,Common components,Model from insurance(CreditRisk+),Credit Metrics,KMV,Model comparison,BankofThailand,2,RiskManagementSymposium -September 2000,BISRegulatory ModelVsCredit RiskModels,BISRisk-Based Capital Requirements,Allprivate-sector loans,(uncollateralized),aresubjected toan8 percent capital reserve requirement, irrespectiveof the sizeof the loan,itsmaturity, and the credit quality oftheborrowing counterparty.,Note,: Some adjustments are madeto,collateralized/guaranteed,loans toOECD governments, banks, and securitiesdealers.,BankofThailand,3,RiskManagementSymposium -September 2000,Credit RiskModels,- CreditRisk+,- CreditMetrics,- KMV,- Othersimilarmodels,BISRegulatory ModelVsCredit RiskModels,BankofThailand,4,RiskManagementSymposium -September 2000,Disadvantages ofBISRegulatoryModel,1. Doesnotcapturecredit-quality differences amongprivate-sectorborrowers,2. Ignores the potentialforcreditriskreduction via loandiversification,These potentially resultintoolarge acapitalrequirement!,BISRegulatory ModelVsCredit RiskModels,BankofThailand,5,RiskManagementSymposium -September 2000,BISRegulatory ModelVsCredit RiskModels,Bigdifference in probability ofdefaultexistsacross differentcreditqualities.,Note,: 1.Probabilityofdefaultis basedon1-year horizon.,2. Historical statisticsfrom Standard &PoorsCreditWeek April15,1996.,BankofThailand,6,RiskManagementSymposium -September 2000,BISRegulatory ModelVsCredit RiskModels,Defaultcorrelationscanhave significant impactonportfolio potentialloss. KMV findsthat correlations typicallylieintherange 0.002to 0.15.,8%,8%,BISmodel requires 8% oftotal.,8%,8%,Correlation= 1,Correlation= 0.15,Actual exposureis only6% of total.,BankofThailand,7,RiskManagementSymposium -September 2000,BISRegulatory ModelVsCredit RiskModels,Thecapitalrequirementto coverunexpectedlossdecreases rapidly as the numberofcounterparties becomes larger.,Unexpected loss,#,of counterparties,1,16,8%,3.54%,Assumption,: All loansareof equalsize, and correlationsbetweendifferent counterpartiesare0.15.,BankofThailand,8,RiskManagementSymposium -September 2000,CurrentIssues in CreditRisk Modelling,Adaptedfrom,“,“CreditRisk Modelling:CurrentPractices and Applications”, April1999, byBasleCommittee onBankingSupervision,BankofThailand,9,RiskManagementSymposium -September 2000,CurrentIssues in CreditRisk Modelling,Adaptedfrom,“,“CreditRisk Modelling:CurrentPractices and Applications”, April1999, byBasleCommittee onBankingSupervision,BankofThailand,10,RiskManagementSymposium -September 2000,CurrentIssues in CreditRisk Modelling,Adaptedfrom,“,“CreditRisk Modelling:CurrentPractices and Applications”, April1999, byBasleCommittee onBankingSupervision,BankofThailand,11,RiskManagementSymposium -September 2000,CurrentIssues in CreditRisk Modelling,Adaptedfrom,“,“CreditRisk Modelling:CurrentPractices and Applications”, April1999, byBasleCommittee onBankingSupervision,BankofThailand,12,RiskManagementSymposium -September 2000,Credit RiskModels,(,A) Purpose of acredit riskmodel,Measuring economic riskcaused by,Defaults,Downratings,Identifyingrisksourcesandtheir contributions,Scenarioanalysis and Stresstest,Economiccapitalrequirementandallocation,Performanceevaluation (e.g.RAROC),BankofThailand,13,RiskManagementSymposium -September 2000,Credit RiskModels,(,B) Common Components,1. Modelstructure,Transaction1,Transaction2,.,Transaction1,Transaction2,.,CounterpartyA,CounterpartyB,Portfolio ofseveralcounterpartiesandtransactions,Correlations,BankofThailand,14,RiskManagementSymposium -September 2000,Credit RiskModels,2.,Quantitativevariables/parameters,- Default probability/intensity(PD,EDF),- Loan equivalent exposure (LEE),- Loss givendefault(LGD),Recoveryrate (RR),Severity(SEV),- Loss distribution,- Expected loss(EL),- Unexpectedloss (UL),Portfolio risk,- Economic capital (EC),- Risk contributions(RC), Contributoryeconomiccapital(CEC),BankofThailand,15,RiskManagementSymposium -September 2000,Credit RiskModels,(,C) Model from Insurance (Credit Risk+),- Only twostates oftheworldareconsidered- defaultand no default.,- Spread changes (both due tomarket movementandrating upgrades/downgrades) are considered part ofmarket risk.,- Defaultprobability ismodeled asa continuous variable.,Bankof Thailand,16,RiskManagementSymposium- September 2000,Credit Risk Models,(,C) Model from Insurance (Credit Risk+),Thereare3 types ofuncertainty:,1. Actualnumber ofdefaults givena mean defaultintensity,2. Mean defaultintensity(only inthe new approach!),3. Severity ofloss,Bankof Thailand,17,RiskManagementSymposium- September 2000,Credit Risk Models,(,C) Model from Insurance (Credit Risk+),The wholeloanportfoliocan be dividedintoclasses, each of which consists ofborrowerswithsimilar defaultrisk. Hence,a portfolio ofloansto each classof borrowers can beviewed asa uniformportfolio.,- m counterparties,- a uniform defaultprobability ofp(m),Bankof Thailand,18,RiskManagementSymposium- September 2000,Credit Risk Models,(,C) Model from Insurance (Credit Risk+),DP,Counterparties,m1, p(m1),m2, p(m2),m3, p(m3),m4, p(m4),Bankof Thailand,19,RiskManagementSymposium- September 2000,Credit Risk Models,(,C) Model from Insurance (Credit Risk+),Within each class ofcounterparties, number of defaultsfollows Poisson Distribution.,m = numberof counterparties,p(m)= uniformdefault probability,n = numberof defaults in1 year,Bankof Thailand,20,RiskManagementSymposium- September 2000,Credit Risk Models,(,C) Model from Insurance (Credit Risk+),If defaultintensity( )is constant, defaults are implicitly assumedto be independent (zerocorrelation).Thisis the oldapproach.,We know that counterparties are somewhatdependent. Asa result,theold approach isnotrealistic(toooptimistic).,Bankof Thailand,21,RiskManagementSymposium- September 2000,Credit Risk Models,(,C) Model from Insurance (Credit Risk+),The new approach incorporatesdependencyof counterparties by assumingthatdefault intensity is random and followsgamma distribution.,defines shape,anddefines scale ofthedistribution.,Default intensity,Probability density,Bankof Thailand,22,RiskManagementSymposium- September 2000,Credit Risk Models,(,C) Model from Insurance (Credit Risk+),Number ofdefaults (n),Default intensity (),Bankof Thailand,23,RiskManagementSymposium- September 2000,Credit Risk Models,(,C) Model from Insurance (Credit Risk+),Defaults are now relatedsincetheyareexposed tothesamedefault intensity.Higher defaultintensityeffects all obligorsin the portfolio.,Firstmoment:,Second moment:,Mean Variance,(Over-dispersion),Bankof Thailand,24,RiskManagementSymposium- September 2000,CreditRiskModels,(,C)ModelfromInsurance(CreditRisk+),NegativeBinomialDistribution(NGD)exhibitsover-dispersionand,“,“fattertails”,whichmakeitclosertorealitythanPoissonDistribution.,#,ofdefaults,Probabilitydensity,Poisson,Negative Binomial,EL(P)=EL(NGD),UL(P)UL(NGD),BankofThailand,25,RiskManagementSymposium-September2000,CreditRiskModels,(,C)ModelfromInsurance(CreditRisk+),Thelastsourceofuncertaintyisthelossamountincaseofdefault(LEE*LGD),Thisismodeledbybucketingintoexposurebandsandidentifyingtheprobabilitythatadefaultedobligorhasalossinagivenbandwiththepercentageofallcounterpartieswithinthisgivenband.,BankofThailand,26,RiskManagementSymposium-September2000,CreditRiskModels,(,C)ModelfromInsurance(CreditRisk+),ProbabilityDistributionofLossAmount,BankofThailand,27,RiskManagementSymposium-September2000,CreditRiskModels,(,C)ModelfromInsurance(CreditRisk+),Probabilitydistributionof#ofdefaults,Probabilitydistributionoflossamount,Theanalyticformulaofthelossdistributionintheformofprobabilitygeneratingfunction(PGF),Probability,EL,UL,andPercentilecanbefound.,BankofThailand,28,RiskManagementSymposium-September2000,CreditRiskModels,(,D)CreditMetrics,-Introducedin1997byJ.P.Morgan.,-Bothdefaultsandspreadchangesduetoratingupgrades/downgradesareincorporated.,-Creditmigration(includingdefault)isdiscrete.,-Allcounterpartieswiththesamecreditratinghavethesameprobabilityofratingupgrades,ratingdowngrades,anddefaults.,BankofThailand,29,RiskManagementSymposium-September2000,CreditRiskModels,(,D)CreditMetrics,Analysisisdoneoneachindividualcounterparty,whichwillthenbecombinedintoaportfolio,usingcorrelations.Therefore,theonlykeytypeofuncertaintymodeledhereisthecreditrating(ordefault)atwhichaparticularcounterpartywillbeoneyearfromnow.,BankofThailand,30,RiskManagementSymposium-September2000,CreditRiskModels,(,D)CreditMetrics,Rating,Time,0,1,BBB,BBB,AAA,B,Default,BankofThailand,31,RiskManagementSymposium-September2000,CreditRiskModels,(,D)CreditMetrics,Inthecounterpartylevel,twoinputsarerequired:,1.Credittransitionmatrix(Moody,s,S&PorKMV),Source,:Standard&Poor,sCreditWeekApril15,1996,BankofThailand,32,RiskManagementSymposium-September2000,CreditRiskModels,(,D)CreditMetrics,2.Spreadmatrixandrecoveryrates,Source,:Carty&Lieberman(96a)-Moody,sInvestorService,BankofThailand,33,RiskManagementSymposium-September2000,CreditRiskModels,(,D)CreditMetrics,Possiblevaluesofloanoneyearfromnowcanthenbecalculated,eachofwhichhasitsownprobability:,Now,theloanisratedBBB.ItsbondequivalentyieldisRf+S,BBB,.,1,year,Bank of Thailand,34,Risk ManagementSymposium- September2000,CreditRiskModels,(,D)CreditMetrics,Loss =V,current,- V,new,EL,UL, Percentile, andVaRcan be found.,E(V),V(1st-percentile),VaR,Bank of Thailand,35,Risk ManagementSymposium- September2000,CreditRiskModels,(,D)CreditMetrics,Intheportfolio level,correlationsare neededtocombine allcounterparties(orloans) andfind theportfoliolossdistribution:,- “Ability to pay”=,“,“Normalizedequityvalue,”,”,- Migrationprobabilities predefinebuckets (lowerandupperthresholds)for thefutureabilitytopay,- Correlation of defaultand migrationscan,hence,bederivedfrom correlation of the,“,“abilitytopay,”,”.,Bank of Thailand,36,Risk ManagementSymposium- September2000,CreditRiskModels,(,D)CreditMetrics,Inordertofind theloss distributionofa 2-counterparty portfolio,weneedtocalculatethe joint migrationprobabilities andthepayoffsforeachpossiblescenario:,Probabilitythat counterparty1 and2 willberatedBBand BBBrespectively,Bank of Thailand,37,Risk ManagementSymposium- September2000,CreditRiskModels,(,D)CreditMetrics,SampleJointTransitionMatrix(assuming0.3 asset correlation),Source,: CreditMetrics-TechnicalDocument, April 2, 1997, p. 38,Bank of Thailand,38,Risk ManagementSymposium- September2000,CreditRiskModels,(,D)CreditMetrics,ForNcounterparties,one waytofind theloss distributionistokeep expandingthejointtransitionmatrix.This,however,rapidly becomescomputationally difficult(the numberofpossiblejointtransition probabilitiesis8,N,).,Another wayistosumcounterparty asset volatilitiesistousethe variance summationequation.Thisisacceptableonly forthelossdistributions thatare close to normal.,Bank of Thailand,39,Risk ManagementSymposium- September2000,Credit RiskModels,(,D) Credit Metrics,Forcomputing the distribution of loan values inthelarge sample case whereloan valuesarenotnormally distributed, Credit Metrics uses MonteCarlo simulation.,TheCredit Metrics portfoliomethodologycanalso beused for calculating the marginal riskcontribution(RC) for individualcounterparties.RCisuseful in identifying the counterpartiestowhich wehave excessiveriskexposure.,BankofThailand,40,RiskManagementSymposium -September 2000,Credit RiskModels,(,D) Credit Metrics,ExposureDistribution,Rating migrationlikelihoods,Spread matrix and recovery rates,Correlations,Joint creditratingchanges,Portfolio componentsandmarketvolatilities,Value and loss distributionof individual obligors,Portfolio valueandlossdistribution,EL,UL,Percentile,andVaRcanbe found.,Summary,BankofThailand,41,RiskManagementSymposium -September 2000,Credit RiskModels,(,E) “KMV-Type,”,” Model,- One orboth defaults and spread changes due toratingupgrades/downgradescanbe incorporated.,- EDF isfirm-specific.,- EDF variescontinuously with firmasset valueandvolatility.,- Potentially acontinuous credit migration.,BankofThailand,42,RiskManagementSymposium -September 2000,Credit RiskModels,(,E) “KMV-Type,”,” Model,Analysisisdoneoneachindividualcounterparty, whichwillthen becombined into aportfolio,using asset-value correlations.Therefore,theonlykeytype ofuncertaintymodeledhere iswhetherornottheasset valueof eachfirm, one year fromnow,will behigherthanthevalue of its liabilities.,BankofThailand,43,RiskManagementSymposium -September 2000,Credit RiskModels,(,E) “KMV-Type,”,” Model,Abilityto pay =Asset value,Time,0,1,Defaultpoint =Value ofliabilities,Asset valuedistribution,Defaultprobability,Value,BankofThailand,44,RiskManagementSymposium -September 2000,Credit RiskModels,(,E) “KMV-Type,”,” Model,Thequestionis,“,“howtofindthedistribution offutureasset value”.,KMVdefinesthedistributionbythemeanasset valueandtheasset volatility (or standard deviation).Thequestionnowbecomes,“,“how tofind the assetvalue and its volatility,”,”.,BankofThailand,45,RiskManagementSymposium -September 2000,Credit RiskModels,(,E) “KMV-Type,”,” Model,Since wecanobserveonly equityvalue and its volatility, the linkbetweenequity and assetvaluesandthatbetweenequityandasset volatilities needto be established.KMVsolve this problem usinganoption pricing model.,BankofThailand,46,RiskManagementSymposium -September 2000,Credit RiskModels,(,E) “KMV-Type,”,” Model,0,Firm value,Liability value,0,Firmvalue,Equity value,Bookvalue of liabilities,Bookvalue of liabilities,Liabilities “Shortput,”,”,Equity ,“,“Long call”,BankofThailand,47,RiskManagementSymposium -September 2000,Credit RiskModels,(,E) “KMV-Type,”,” Model,Equity is like acall optiononthefirmasset:,Twounknowns(and)canbe solved from thesetwoequations.,BankofThailand,48,RiskManagementSymposium -September 2000,Credit RiskModels,(,E) “KMV-Type,”,” Model,Distancetodefault(DD)isthencalculated:,Since the assetvalue distribution is not normal, KMV linksDD to EDF usinghistorical relationship.,BankofThailand,49,RiskManagementSymposium -September 2000,Credit RiskModels,(,E) “KMV-Type,”,” Model,KMVclaims thatfora givenDD,EDFis remarkably constant across key variables:,- Industry/sector,- Company size,- Time,Thisprovides arobust basisforDD-EDFmapping.,BankofThailand,50,RiskManagementSymposium -September 2000,Credit RiskModels,(,E) “KMV-Type,”,” Model,LikeCreditMetrics,correlations are neededtocombineallcounterparties (or loans) into aportfolio and findtheportfolio loss distribution:,- “Ability to pay” =,“,“Marketvalue of the firm asset,”,”,- EDF isdefinedasa chancethat the “ability to pay” willreach the default point.,- Correlation ofdefaultcan, hence,bederivedfromcorrelationofasset value.,BankofThailand,51,RiskManagementSymposium -September 2000,Credit RiskModels,(,E) “KMV-Type,”,” Model,For2 counterparties, the jointdefaultprobabilitycanbe calculated asfollows:,Fora largenumber of counterparties, jointprobabilities couldbecome computationally difficult(the numberofjoint probabilitiesis 2,N,).,BankofThailand,52,RiskManagementSymposium-September2000,CreditRiskModels,(,E),“,“KMV-Type,”,”Model,Whenthelossdistributionisclosetonormal,thevariancesummationequationcanbeused.Inothercases,MonteCarlosimulationmaybeabetterapproach.,RCcanbecalculatedusing,“,“incremental,”,”approach.Thisistoanswerthequestion:,“,“howmuchwillanincrementalamountofnewloansmadetoacurrentborrowerincreasetheportfoliorisk?,”,”.TheKMVmodelcanalsobeusedtofindthecreditefficientfrontieraswellastheRAROC.,BankofThailand,53,RiskManagementSymposium-September2000,CreditRiskModels,(,E),“,“KMV-Type,”,”Model,Summary,(defaultmode),Exposure Distribution,EDF,Recovery rates,Correlations,Joint default probabilities,Portfolio components and market volatilities,EL and UL of individual obligors,Portfolio value and loss distribution,EL, UL, Percentile, and VaR can be found.,Equity value and volatility,Financial Structure,BankofThailand,54,RiskManagementSymposium-September2000,ModelComparison,BankofThailand,55,RiskManagementSymposium- September 2000,ModelComparison,Bankof Thailand,56,RiskManagementSymposium- September 2000,Reference,Saunders,Anthony, Credit Risk Measurement,“,“NewApproaches toValue-at-Risk and Other Paradigms,JohnWiley& Sons, Inc.,1999,Credit Metrics,- Technical Document, April 2,1997,KMV Corporation, ModelingDefault Risk,revised January12,1997,Overbeck,Ludger, “CreditRiskModelling”Presentation,August 3,2000,Jones, David, and John Mingo, IndustryPracticesin CreditRiskModelingand Internal CapitalAllocations: Implications fora Models-BasedRegulatory CapitalStandard,Economic PolicyReview, Federal ReserveBankof New York, October1998,BasleCommitteeon Banking Supervision, Credit Risk Modelling:Current Practices and Applications,April 1999,Bankof Thailand,57,RiskManagementSymposium- September 2000,
展开阅读全文