1、Issues in Credit Risk ModellingRisk Management SymposiumSeptember 2,2000Bank of ThailandChotibhak JotikasthiraBank of ThailandRisk Management Symposium -September 2000Page 2Overview BIS regulatory model Vs Credit risk models Current Issues in Credit Risk Modelling Brief introduction to credit risk m
2、odels Purpose of a credit risk model Common components Model from insurance(Credit Risk+)Credit Metrics KMV Model comparisonBank of ThailandRisk Management Symposium -September 2000Page 3BIS Regulatory Model Vs Credit Risk ModelsBIS Risk-Based Capital RequirementsAll private-sector loans(uncollatera
3、lized)are subjected to an 8 percent capital reserve requirement,irrespective of the size of the loan,its maturity,and the credit quality of the borrowing counterparty.Note:Some adjustments are made to collateralized/guaranteed loans to OECD governments,banks,and securities dealers.Bank of ThailandRi
4、sk Management Symposium -September 2000Page 4Credit Risk Models-Credit Risk+-Credit Metrics-KMV-Other similar modelsBIS Regulatory Model Vs Credit Risk ModelsBank of ThailandRisk Management Symposium -September 2000Page 5Disadvantages of BIS Regulatory Model1.Does not capture credit-quality differen
5、ces among private-sector borrowers2.Ignores the potential for credit risk reduction via loan diversificationThese potentially result in too large a capital requirement!BIS Regulatory Model Vs Credit Risk ModelsBank of ThailandRisk Management Symposium -September 2000Page 6BIS Regulatory Model Vs Cre
6、dit Risk ModelsBig difference in probability of default exists across different credit qualities.Credit Rating Probability of DefaultAAA0.00%AA0.00%A0.06%Credit Rating Probability of DefaultBBB0.18%BB1.06%B5.20%CCC19.79%Note:1.Probability of default is based on 1-year horizon.2.Historical statistics
7、 from Standard&Poors CreditWeek April 15,1996.Bank of ThailandRisk Management Symposium -September 2000Page 7BIS Regulatory Model Vs Credit Risk ModelsDefault correlations can have significant impact on portfolio potential loss.KMV finds that correlations typically lie in the range 0.002 to 0.15.8%8
8、%BIS model requires 8%of total.8%8%Correlation=1Correlation=0.15Actual exposure is only 6%of total.Bank of ThailandRisk Management Symposium -September 2000Page 8BIS Regulatory Model Vs Credit Risk ModelsThe capital requirement to cover unexpected loss decreases rapidly as the number of counterparti
9、es becomes larger.Unexpected loss#of counterparties1168%3.54%Assumption:All loans are of equal size,and correlations between different counterparties are 0.15.Bank of ThailandRisk Management Symposium -September 2000Page 9Current Issues in Credit Risk ModellingAdapted from“Credit Risk Modelling:Curr
10、ent Practices and Applications”,April 1999,by Basle Committee on Banking SupervisionTopicConceptual Issues/ConcernsDefinition of riskShould credit risk include only default or both default and rating migrations?Is there a material difference between the default mode and the mark-to-market mode model
11、s?Risk driversWhen does default actually occur?In the threshold models,what observable variable should be used to represent ability to pay?Model conceptIs the model that starts from a pool of similar loans or obligors realistic?Pooled data usually hide credit specific risks.Probability density funct
12、ionNo agreement on the family of distributions to use.Loss distribution is not normal;it empirically has fatter tails.Correlation of credit eventsHow should co-movement among rating migrations and defaults be modeled?Implicit or explicit?Conditional Vs UnconditionalCurrently,most models are uncondit
13、ional(independent from the state of economy).Using these models,risk can understated or overstated depending on the location within the business cycle?Bank of ThailandRisk Management Symposium -September 2000Page 10Current Issues in Credit Risk ModellingAdapted from“Credit Risk Modelling:Current Pra
14、ctices and Applications”,April 1999,by Basle Committee on Banking SupervisionTopicParameter Specification Issues/ConcernsLoss given default(LGD)LGD is random;hence,a distribution is needed to represent LGD.Lack of sensitivity analysis with respect to LGD.Lack of historical data to validate currently
15、 used models.Risk ratings,expected default frequency(EDF),and migration probabilitiesIn determining EDF and migration probabilities,Internal rating systems may not be accurate or have enough history.EDF and migration probabilities of publicly traded bonds may not be accurate for bank credits.Most sy
16、stems combine EDF and LGD.Migration and default correlationsIs it reasonable to use equity information to estimate correlations for bank credits?Lack of historical data to validate models used to estimate this parameter.Bank of ThailandRisk Management Symposium -September 2000Page 11Current Issues i
17、n Credit Risk ModellingAdapted from“Credit Risk Modelling:Current Practices and Applications”,April 1999,by Basle Committee on Banking SupervisionTopicParameter Specification Issues/ConcernsCredit spreadsFor Mark-to-Market models,how much spread should be used to value loans at each credit rating?Ar
18、e the forward spreads(based on today yield curve)a good approximation of the future spreads?How is liquidity element of credit spreads taken into account?Exposure levels Different instruments(especially market driven instruments)have different levels of risk exposure(e.g.swaps vs loans).Estimates ar
19、e made to make different instruments comparable.The accuracy of estimates is questionable.Computational requirementSome models are computationally intensive.Bank of ThailandRisk Management Symposium -September 2000Page 12Current Issues in Credit Risk ModellingAdapted from“Credit Risk Modelling:Curre
20、nt Practices and Applications”,April 1999,by Basle Committee on Banking SupervisionTopicValidation Issues/ConcernsBacktestingTo date,there is no way to verify accuracy.Limited availability of historical data is a big hurdle.Given a limited history,the question is how to adequately backtest.Stress te
21、stingStress testing should be used at least to partially compensate for short-comings in available backtesting methods.Few institutions are doing stress testings.Sensitivity analysisThe extreme tail of the probability density function is likely to be highly sensitive to key assumptions and to estima
22、tes of key parameters.Sensitivity analysis is,therefore,crucial in validating a model.Very limited work has been completed in this area to date.Bank of ThailandRisk Management Symposium -September 2000Page 13Credit Risk Models(A)Purpose of a credit risk model Measuring economic risk caused by Defaul
23、ts Downratings Identifying risk sources and their contributions Scenario analysis and Stress test Economic capital requirement and allocation Performance evaluation(e.g.RAROC)Bank of ThailandRisk Management Symposium -September 2000Page 14Credit Risk Models(B)Common Components1.Model structureTransa
24、ction 1Transaction 2.Transaction 1Transaction 2.Counterparty ACounterparty BPortfolio of several counterparties and transactionsCorrelationsBank of ThailandRisk Management Symposium -September 2000Page 15Credit Risk Models2.Quantitative variables/parameters-Default probability/intensity(PD,EDF)-Loan
25、 equivalent exposure(LEE)-Loss given default(LGD),Recovery rate(RR),Severity(SEV)-Loss distribution-Expected loss(EL)-Unexpected loss(UL),Portfolio risk-Economic capital(EC)-Risk contributions(RC),Contributory economic capital(CEC)Bank of ThailandRisk Management Symposium -September 2000Page 16Credi
26、t Risk Models(C)Model from Insurance(Credit Risk+)-Only two states of the world are considered-default and no default.-Spread changes(both due to market movement and rating upgrades/downgrades)are considered part of market risk.-Default probability is modeled as a continuous variable.Bank of Thailan
27、dRisk Management Symposium -September 2000Page 17Credit Risk Models(C)Model from Insurance(Credit Risk+)There are 3 types of uncertainty:1.Actual number of defaults given a mean default intensity2.Mean default intensity(only in the new approach!)3.Severity of loss Bank of ThailandRisk Management Sym
28、posium -September 2000Page 18Credit Risk Models(C)Model from Insurance(Credit Risk+)The whole loan portfolio can be divided into classes,each of which consists of borrowers with similar default risk.Hence,a portfolio of loans to each class of borrowers can be viewed as a uniform portfolio.-m counter
29、parties-a uniform default probability of p(m)Bank of ThailandRisk Management Symposium -September 2000Page 19Credit Risk Models(C)Model from Insurance(Credit Risk+)DPCounterpartiesm1,p(m1)m2,p(m2)m3,p(m3)m4,p(m4)Bank of ThailandRisk Management Symposium -September 2000Page 20Credit Risk Models(C)Mod
30、el from Insurance(Credit Risk+)Within each class of counterparties,number of defaults follows Poisson Distribution.!)(nenPnmmp*)(m=number of counterpartiesp(m)=uniform default probabilityn=number of defaults in 1 yearBank of ThailandRisk Management Symposium -September 2000Page 21Credit Risk Models(
31、C)Model from Insurance(Credit Risk+)If default intensity()is constant,defaults are implicitly assumed to be independent(zero correlation).This is the old approach.We know that counterparties are somewhat dependent.As a result,the old approach is not realistic(too optimistic).Bank of ThailandRisk Man
32、agement Symposium -September 2000Page 22Credit Risk Models(C)Model from Insurance(Credit Risk+)The new approach incorporates dependency of counterparties by assuming that default intensity is random and follows gamma distribution.),(defines shape,and defines scale of the distribution.Default intensi
33、tyProbability densityBank of ThailandRisk Management Symposium -September 2000Page 23Credit Risk Models(C)Model from Insurance(Credit Risk+)Number of defaults(n)Default intensity(),()(Poissonn),(nomialNegativeBinBank of ThailandRisk Management Symposium -September 2000Page 24Credit Risk Models(C)Mod
34、el from Insurance(Credit Risk+)Defaults are now related since they are exposed to the same default intensity.Higher default intensity effects all obligors in the portfolio.First moment:Second moment:)(nE)1()(nVMean Variance(Over-dispersion)Bank of ThailandRisk Management Symposium -September 2000Pag
35、e 25Credit Risk Models(C)Model from Insurance(Credit Risk+)Negative Binomial Distribution(NGD)exhibits over-dispersion and“fatter tails”,which make it closer to reality than Poisson Distribution.#of defaultsProbability densityPoissonNegative BinomialEL(P)=EL(NGD)UL(P)UL(NGD)Bank of ThailandRisk Mana
36、gement Symposium -September 2000Page 26Credit Risk Models(C)Model from Insurance(Credit Risk+)The last source of uncertainty is the loss amount in case of default(LEE*LGD)This is modeled by bucketing into exposure bands and identifying the probability that a defaulted obligor has a loss in a given b
37、and with the percentage of all counterparties within this given band.Bank of ThailandRisk Management Symposium -September 2000Page 27Credit Risk Models(C)Model from Insurance(Credit Risk+)0%10%20%30%40%50%Under 5050 to 100100 to 200Over 200Loss amountProbabilityProbability Distribution of Loss Amoun
38、tBank of ThailandRisk Management Symposium -September 2000Page 28Credit Risk Models(C)Model from Insurance(Credit Risk+)Probability distribution of#of defaults0%10%20%30%40%50%Under 5050 to 100100 to 200Over 200Loss amountProbabilityProbability distribution of loss amountThe analytic formula of the
39、loss distribution in the form of probability generating function(PGF)Probability,EL,UL,and Percentile can be found.Bank of ThailandRisk Management Symposium -September 2000Page 29Credit Risk Models(D)Credit Metrics-Introduced in 1997 by J.P.Morgan.-Both defaults and spread changes due to rating upgr
40、ades/downgrades are incorporated.-Credit migration(including default)is discrete.-All counterparties with the same credit rating have the same probability of rating upgrades,rating downgrades,and defaults.Bank of ThailandRisk Management Symposium -September 2000Page 30Credit Risk Models(D)Credit Met
41、ricsAnalysis is done on each individual counterparty,which will then be combined into a portfolio,using correlations.Therefore,the only key type of uncertainty modeled here is the credit rating(or default)at which a particular counterparty will be one year from now.Bank of ThailandRisk Management Sy
42、mposium -September 2000Page 31Credit Risk Models(D)Credit MetricsRatingTime01BBBBBBAAABDefaultBank of ThailandRisk Management Symposium -September 2000Page 32Credit Risk Models(D)Credit MetricsIn the counterparty level,two inputs are required:1.Credit transition matrix(Moodys,S&P or KMV)InitialRatin
43、gAAAAAABBBBBBCCCDAAA90.818.330.680.060.12000AA0.790.657.790.640.060.140.020A0.092.2791.055.520.740.260.010.06BBB0.020.335.9586.935.31.170.120.18BB0.030.140.677.7380.538.8411.06B00.110.240.436.4883.644.075.2CCC0.2200.221.32.3811.2464.8619.79Rating at Year-End(%)Source:Standard&Poors CreditWeek April
44、15,1996Bank of ThailandRisk Management Symposium -September 2000Page 33Credit Risk Models(D)Credit Metrics2.Spread matrix and recovery ratesSource:Carty&Lieberman(96a)-Moodys Investor ServiceCreditCreditRatingSpreadAAASAAAAASAAASABBBSBBBBBSBBBSBCCCSCCCMean(%)STD(%)Senior secured53.826.86Senior unsec
45、ured51.1325.45Senior subordinated38.5223.81Subordinated32.7420.18Junior subordinated17.0910.9Seniority ClassRecovery RateBank of ThailandRisk Management Symposium -September 2000Page 34Credit Risk Models(D)Credit MetricsPossible values of loan one year from now can then be calculated,each of which h
46、as its own probability:CreditInterestLoanProbabailityRatingRateValue(%)AAARf+SAAA1100.02AARf+SAA1090.33ARf+SA1085.95BBBRf+SBBB10786.93BBRf+SBB1025.3BRf+SB981.17CCCRf+SCCC840.12Default1-RR510.18Now,the loan is rated BBB.Its bond equivalent yield is Rf+SBBB.1 yearBank of ThailandRisk Management Sympos
47、ium -September 2000Page 35Credit Risk Models(D)Credit Metrics0204060801006080100120Loan valueProbability(%)Loss=Vcurrent-VnewEL,UL,Percentile,and VaR can be found.E(V)V(1st-percentile)VaRBank of ThailandRisk Management Symposium -September 2000Page 36Credit Risk Models(D)Credit MetricsIn the portfol
48、io level,correlations are needed to combine all counterparties(or loans)and find the portfolio loss distribution:-“Ability to pay”=“Normalized equity value”-Migration probabilities predefine buckets(lower and upper thresholds)for the future ability to pay-Correlation of default and migrations can,he
49、nce,be derived from correlation of the“ability to pay”.Bank of ThailandRisk Management Symposium -September 2000Page 37Credit Risk Models(D)Credit MetricsIn order to find the loss distribution of a 2-counterparty portfolio,we need to calculate the joint migration probabilities and the payoffs for ea
50、ch possible scenario:BBZBZAZBBBZABBBBBBdrdrrrfZrZZrZP212121);,(),(Probability that counterparty 1 and 2 will be rated BB and BBB respectivelyBank of ThailandRisk Management Symposium -September 2000Page 38Credit Risk Models(D)Credit MetricsAAAAAABBBBBBCCCDefault0.092.2791.055.520.740.260.010.06AAA0.
