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1、Issues in Credit Risk ModellingRisk Management SymposiumSeptember 2,2000Bank of ThailandChotibhak Jotikasthira1OverviewBIS regulatory model Vs Credit risk modelsCurrent Issues in Credit Risk ModellingBrief introduction to credit risk modelsPurpose of a credit risk modelCommon componentsModel from in
2、surance(Credit Risk+)Credit MetricsKMVModel comparisonBank of Thailand2Risk 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,irrespecti
3、ve 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 Thailand3Risk Management Symposium -September 2000Credit Risk Models-Credit Risk+-Cr
4、edit Metrics-KMV-Other similar modelsBIS Regulatory Model Vs Credit Risk ModelsBank of Thailand4Risk 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
5、via loan diversificationThese potentially result in too large a capital requirement!BIS Regulatory Model Vs Credit Risk ModelsBank of Thailand5Risk Management Symposium -September 2000BIS Regulatory Model Vs Credit Risk ModelsBig difference in probability of default exists across different credit qu
6、alities.Note:1.Probability of default is based on 1-year horizon.2.Historical statistics from Standard&Poors CreditWeek April 15,1996.Bank of Thailand6Risk Management Symposium -September 2000BIS Regulatory Model Vs Credit Risk ModelsDefault correlations can have significant impact on portfolio pote
7、ntial 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 Thailand7Risk Management Symposium -September 2000BIS Regulatory Model Vs Credit Risk ModelsThe capital requir
8、ement 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 Thailand8Risk Management Symposium -September 2000Curre
9、nt Issues in Credit Risk ModellingAdapted from“Credit Risk Modelling:Current Practices and Applications”,April 1999,by Basle Committee on Banking SupervisionBank of Thailand9Risk Management Symposium -September 2000Current Issues in Credit Risk ModellingAdapted from“Credit Risk Modelling:Current Pra
10、ctices and Applications”,April 1999,by Basle Committee on Banking SupervisionBank of Thailand10Risk Management Symposium -September 2000Current Issues in Credit Risk ModellingAdapted from“Credit Risk Modelling:Current Practices and Applications”,April 1999,by Basle Committee on Banking SupervisionBa
11、nk of Thailand11Risk 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 Thailand12Risk Management Symposium -September 2000Credit Risk Models(A)P
12、urpose of a credit risk modelMeasuring economic risk caused byDefaultsDownratingsIdentifying risk sources and their contributionsScenario analysis and Stress testEconomic capital requirement and allocationPerformance evaluation(e.g.RAROC)Bank of Thailand13Risk Management Symposium -September 2000Cre
13、dit Risk Models(B)Common Components 1.Model structureTransaction 1Transaction 2.Transaction 1Transaction 2.Counterparty ACounterparty BPortfolio of several counterparties and transactionsCorrelationsBank of Thailand14Risk Management Symposium -September 2000Credit Risk Models2.Quantitative variables
14、/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 Thailan
15、d15Risk 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
16、 modeled as a continuous variable.Bank of Thailand16Risk 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
17、 of loss Bank of Thailand17Risk 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 v
18、iewed as a uniform portfolio.-m counterparties-a uniform default probability of p(m)Bank of Thailand18Risk 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 Thailand19Risk Management Symposium -September
19、 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 Thailand20Risk Management Symposium -September 2000Credit Ri
20、sk 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 Thaila
21、nd21Risk 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 inten
22、sityProbability densityBank of Thailand22Risk Management Symposium -September 2000Credit Risk Models(C)Model from Insurance(Credit Risk+)Number of defaults(n)Default intensity()Bank of Thailand23Risk Management Symposium -September 2000Credit Risk Models(C)Model from Insurance(Credit Risk+)Defaults
23、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 Thailand24Risk Management Symposium -September 2000Credit Risk Models(C)Model from Insurance(Credit Ris
24、k+)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 Thailand25Risk Management Symposium -September 2000Credit Risk Models(C)M
25、odel 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 giv
26、en band.Bank of Thailand26Risk Management Symposium -September 2000Credit Risk Models(C)Model from Insurance(Credit Risk+)Probability Distribution of Loss AmountBank of Thailand27Risk Management Symposium -September 2000Credit Risk Models(C)Model from Insurance(Credit Risk+)Probability distribution
27、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 Thailand28Risk Management Symposium -September 2000Credit Risk Models(D)Credit Metrics-Introduce
28、d 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 Thailand29R
29、isk 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 co
30、unterparty will be one year from now.Bank of Thailand30Risk Management Symposium -September 2000Credit Risk Models(D)Credit Metrics RatingTime01BBBBBBAAABDefaultBank of Thailand31Risk Management Symposium -September 2000Credit Risk Models(D)Credit MetricsIn the counterparty level,two inputs are requ
31、ired:1.Credit transition matrix(Moodys,S&P or KMV)Source:Standard&Poors CreditWeek April 15,1996Bank of Thailand32Risk Management Symposium -September 2000Credit Risk Models(D)Credit Metrics2.Spread matrix and recovery ratesSource:Carty&Lieberman(96a)-Moodys Investor ServiceBank of Thailand33Risk Ma
32、nagement 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 Thailand34Risk Management Symposium -September 2000
33、Credit Risk Models(D)Credit MetricsLoss=Vcurrent-VnewEL,UL,Percentile,and VaR can be found.E(V)V(1st-percentile)VaRBank of Thailand35Risk Management Symposium -September 2000Credit Risk Models(D)Credit MetricsIn the portfolio level,correlations are needed to combine all counterparties(or loans)and f
34、ind 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 Thailand36Risk
35、 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 BB
36、B respectivelyBank of Thailand37Risk 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 Thailand38Risk Management Symposium -September 2000Credit Risk M
37、odels(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
38、is to use the variance summation equation.This is acceptable only for the loss distributions that are close to normal.Bank of Thailand39Risk Management Symposium -September 2000Credit Risk Models(D)Credit MetricsFor computing the distribution of loan values in the large sample case where loan values
39、 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.B
40、ank of Thailand40Risk Management Symposium -September 2000Credit Risk Models(D)Credit Metrics Exposure DistributionRating migration likelihoodsSpread matrix and recovery ratesCorrelationsJoint credit rating changesPortfolio components and market volatilitiesValue and loss distribution of individual
41、obligorsPortfolio value and loss distributionEL,UL,Percentile,and VaR can be found.SummaryBank of Thailand41Risk 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-specifi
42、c.-EDF varies continuously with firm asset value and volatility.-Potentially a continuous credit migration.Bank of Thailand42Risk Management Symposium -September 2000Credit Risk Models(E)“KMV-Type”ModelAnalysis is done on each individual counterparty,which will then be combined into a portfolio,usin
43、g 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 Thailand43Risk Management Symposium -September 2000Credit Risk Models(E)“KMV-Type”ModelAbility
44、to pay=Asset valueTime01Default point=Value of liabilitiesAsset value distributionDefault probabilityValueBank of Thailand44Risk 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
45、 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 Thailand45Risk Management Symposium -September 2000Credit Risk Models(E)“KMV-Type”ModelSince we can observe only equity value and its volatility,the
46、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 Thailand46Risk Management Symposium -September 2000Credit Risk Models(E)“KMV-Type”Model0Firm valueLiability value0Firm valueEquity v
47、alueBook value of liabilitiesBook value of liabilitiesLiabilities “Short put”Equity “Long call”Bank of Thailand47Risk 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 o
48、f Thailand48Risk 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 Thailand49Risk Management Symposium -September 2000Credit Risk
49、 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 Thailand50Risk Management Symposium -September 2000Credit Risk Models(E)“KMV-Type”ModelLike Credit Metrics
50、,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 reach the default point.-Correlation of default can,hence,be derived fr