信用风险模型.pptx
Issues in Credit Risk ModellingRisk Management SymposiumSeptember 2,2000Bank of Thailand Chotibhak Jotikasthira1Overview BIS regulatory model Vs Credit risk models Current Issues in Credit Risk Modelling Brief introduction to credit risk models Purpose of a credit risk model Common components Model from insurance(Credit Risk+)Credit Metrics KMV Model comparisonBank of Thailand 2 Risk Management Symposium-September 2000BIS Regulatory Model Vs Credit Risk ModelsBIS Risk-Based Capital Requirements All private-sector loans(uncollateralized)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 Thailand 3 Risk Management Symposium-September 2000Credit Risk Models-Credit Risk+-Credit Metrics-KMV-Other similar modelsBIS Regulatory Model Vs Credit Risk ModelsBank of Thailand 4 Risk Management Symposium-September 2000Disadvantages of BIS Regulatory Model1.Does not capture credit-quality differences 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 Thailand 5 Risk Management Symposium-September 2000BIS Regulatory Model Vs Credit Risk ModelsBig difference in probability of default exists across different credit qualities.Note:1.Probability of default is based on 1-year horizon.2.Historical statistics from Standard&Poors CreditWeek April 15,1996.Bank of Thailand 6 Risk Management Symposium-September 2000BIS 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%BIS model requires 8%of total.8%8%Correlation=1Correlation=0.15Actual exposure is only 6%of total.Bank of Thailand 7 Risk Management Symposium-September 2000BIS Regulatory Model Vs Credit Risk ModelsThe capital requirement to cover unexpected loss decreases rapidly as the number of counterparties 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 Thailand 8 Risk Management Symposium-September 2000Current Issues in Credit Risk ModellingAdapted from“Credit Risk Modelling:Current Practices and Applications”,April 1999,by Basle Committee on Banking SupervisionBank of Thailand 9 Risk Management Symposium-September 2000Current Issues in Credit Risk ModellingAdapted from“Credit Risk Modelling:Current Practices and Applications”,April 1999,by Basle Committee on Banking SupervisionBank of Thailand 10 Risk Management Symposium-September 2000Current Issues in Credit Risk ModellingAdapted from“Credit Risk Modelling:Current Practices and Applications”,April 1999,by Basle Committee on Banking SupervisionBank of Thailand 11 Risk Management Symposium-September 2000Current Issues in Credit Risk ModellingAdapted from“Credit Risk Modelling:Current Practices and Applications”,April 1999,by Basle Committee on Banking SupervisionBank of Thailand 12 Risk Management Symposium-September 2000Credit Risk Models(A)Purpose of a credit risk model Measuring economic risk caused by Defaults Downratings Identifying risk sources and their contributions Scenario analysis and Stress test Economic capital requirement and allocation Performance evaluation(e.g.RAROC)Bank of Thailand 13 Risk Management Symposium-September 2000Credit Risk Models(B)Common Components 1.Model structureTransaction 1Transaction 2.Transaction 1Transaction 2.Counterparty ACounterparty BPortfolio of several counterparties and transactionsCorrelationsBank of Thailand 14 Risk Management Symposium-September 2000Credit Risk Models2.Quantitative variables/parameters-Default probability/intensity(PD,EDF)-Loan 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 Thailand 15 Risk Management Symposium-September 2000Credit 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 Thailand 16 Risk Management Symposium-September 2000Credit 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 Thailand 17 Risk Management Symposium-September 2000Credit 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 counterparties-a uniform default probability of p(m)Bank of Thailand 18 Risk Management Symposium-September 2000Credit Risk Models(C)Model from Insurance(Credit Risk+)DPCounterpartiesm1,p(m1)m2,p(m2)m3,p(m3)m4,p(m4)Bank of Thailand 19 Risk Management Symposium-September 2000Credit Risk Models(C)Model from Insurance(Credit Risk+)Within each class of counterparties,number of defaults follows Poisson Distribution.m=number of counterpartiesp(m)=uniform default probabilityn=number of defaults in 1 yearBank of Thailand 20 Risk Management Symposium-September 2000Credit Risk Models(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 Thailand 21 Risk Management Symposium-September 2000Credit 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 intensityProbability densityBank of Thailand 22 Risk Management Symposium-September 2000Credit Risk Models(C)Model from Insurance(Credit Risk+)Number of defaults(n)Default intensity()Bank of Thailand 23 Risk Management Symposium-September 2000Credit Risk Models(C)Model 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:Mean Variance(Over-dispersion)Bank of Thailand 24 Risk Management Symposium-September 2000Credit 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 densityPoisson Negative BinomialEL(P)=EL(NGD)UL(P)UL(NGD)Bank of Thailand 25 Risk Management Symposium-September 2000Credit 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 band with the percentage of all counterparties within this given band.Bank of Thailand 26 Risk Management Symposium-September 2000Credit Risk Models(C)Model from Insurance(Credit Risk+)Probability Distribution of Loss AmountBank of Thailand 27 Risk Management Symposium-September 2000Credit Risk Models(C)Model from Insurance(Credit Risk+)Probability distribution of#of defaultsProbability distribution of loss amountThe analytic formula of the loss distribution in the form of probability generating function(PGF)Probability,EL,UL,and Percentile can be found.Bank of Thailand 28 Risk Management Symposium-September 2000Credit Risk Models(D)Credit Metrics-Introduced in 1997 by J.P.Morgan.-Both defaults and spread changes due to rating upgrades/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 Thailand 29 Risk Management Symposium-September 2000Credit Risk Models(D)Credit MetricsAnalysis 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 Thailand 30 Risk Management Symposium-September 2000Credit Risk Models(D)Credit Metrics RatingTime0 1BBBBBBAAABDefaultBank of Thailand 31 Risk Management Symposium-September 2000Credit Risk Models(D)Credit MetricsIn the counterparty level,two inputs are required:1.Credit transition matrix(Moodys,S&P or KMV)Source:Standard&Poors CreditWeek April 15,1996Bank of Thailand 32 Risk Management Symposium-September 2000Credit Risk Models(D)Credit Metrics2.Spread matrix and recovery ratesSource:Carty&Lieberman(96a)-Moodys Investor ServiceBank of Thailand 33 Risk Management Symposium-September 2000Credit Risk Models(D)Credit MetricsPossible values of loan one year from now can then be calculated,each of which has its own probability:Now,the loan is rated BBB.Its bond equivalent yield is Rf+SBBB.1 yearBank of Thailand 34 Risk Management Symposium-September 2000Credit Risk Models(D)Credit MetricsLoss=Vcurrent-VnewEL,UL,Percentile,and VaR can be found.E(V)V(1st-percentile)VaRBank of Thailand 35 Risk Management Symposium-September 2000Credit Risk Models(D)Credit MetricsIn the portfolio 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,hence,be derived from correlation of the“ability to pay”.Bank of Thailand 36 Risk Management Symposium-September 2000Credit 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 each possible scenario:Probability that counterparty 1 and 2 will be rated BB and BBB respectivelyBank of Thailand 37 Risk Management Symposium-September 2000Credit Risk Models(D)Credit MetricsSample Joint Transition Matrix(assuming 0.3 asset correlation)Source:Credit Metrics-Technical Document,April 2,1997,p.38Bank of Thailand 38 Risk Management Symposium-September 2000Credit Risk Models(D)Credit MetricsFor N counterparties,one way to find the loss distribution is to keep expanding the joint transition matrix.This,however,rapidly becomes computationally difficult(the number of possible joint transition probabilities is 8N).Another way is to sum counterparty asset volatilities is to use the variance summation equation.This is acceptable only for the loss distributions that are close to normal.Bank of Thailand 39 Risk Management Symposium-September 2000Credit Risk Models(D)Credit MetricsFor computing the distribution of loan values in the large sample case where loan values are not normally distributed,Credit Metrics uses Monte Carlo simulation.The Credit Metrics portfolio methodology can also be used for calculating the marginal risk contribution(RC)for individual counterparties.RC is useful in identifying the counterparties to which we have excessive risk exposure.Bank of Thailand 40 Risk Management Symposium-September 2000Credit Risk Models(D)Credit Metrics Exposure DistributionRating migration likelihoodsSpread matrix and recovery rates CorrelationsJoint credit rating changesPortfolio components and market volatilitiesValue and loss distribution of individual obligorsPortfolio value and loss distributionEL,UL,Percentile,and VaR can be found.SummaryBank of Thailand 41 Risk Management Symposium-September 2000Credit Risk Models(E)“KMV-Type”Model-One or both defaults and spread changes due to rating upgrades/downgrades can be incorporated.-EDF is firm-specific.-EDF varies continuously with firm asset value and volatility.-Potentially a continuous credit migration.Bank of Thailand 42 Risk Management Symposium-September 2000Credit Risk Models(E)“KMV-Type”ModelAnalysis is done on each individual counterparty,which will then be combined into a portfolio,using asset-value correlations.Therefore,the only key type of uncertainty modeled here is whether or not the asset value of each firm,one year from now,will be higher than the value of its liabilities.Bank of Thailand 43 Risk Management Symposium-September 2000Credit Risk Models(E)“KMV-Type”ModelAbility to pay=Asset valueTime0 1Default point=Value of liabilitiesAsset value distributionDefault probabilityValueBank of Thailand 44 Risk Management Symposium-September 2000Credit Risk Models(E)“KMV-Type”ModelThe question is“how to find the distribution of future asset value”.KMV defines the distribution by the mean asset value and the asset volatility(or standard deviation).The question now becomes“how to find the asset value and its volatility”.Bank of Thailand 45 Risk Management Symposium-September 2000Credit Risk Models(E)“KMV-Type”ModelSince we can observe only equity value and its volatility,the link between equity and asset values and that between equity and asset volatilities need to be established.KMV solve this problem using an option pricing model.Bank of Thailand 46 Risk Management Symposium-September 2000Credit Risk Models(E)“KMV-Type”Model0Firm valueLiability value0Firm valueEquity valueBook value of liabilities Book value of liabilitiesLiabilities“Short put”Equity“Long call”Bank of Thailand 47 Risk Management Symposium-September 2000Credit Risk Models(E)“KMV-Type”ModelEquity is like a call option on the firm asset:Two unknowns(and)can be solved from these two equations.Bank of Thailand 48 Risk Management Symposium-September 2000Credit Risk Models(E)“KMV-Type”ModelDistance to default(DD)is then calculated:Since the asset value distribution is not normal,KMV links DD to EDF using historical relationship.Bank of Thailand 49 Risk Management Symposium-September 2000Credit Risk Models(E)“KMV-Type”ModelKMV claims that for a given DD,EDF is remarkably constant across key variables:-Industry/sector-Company size-TimeThis provides a robust basis for DD-EDF mapping.Bank of Thailand 50 Risk Management Symposium-September 2000Credit Risk Models(E)“KMV-Type”ModelLike Credit Metrics,correlations are needed to combine all counterparties(or loans)into a portfolio and find the portfolio loss distribution:-“Ability to pay”=“Market value of the firm asset”-EDF is defined as a chance that the“ability to pay”will reac
