信用風(fēng)險模型課件

1、Issues in Credit Risk ModellingRisk Management SymposiumSeptember 2, 2000Bank of ThailandChotibhak JotikasthiraIssues in Credit Risk ModellinBank of ThailandRisk Management Symposium - September 2000Page 2OverviewBIS regulatory model Vs Credit risk modelsCurrent Issues in Credit Risk ModellingBrief

2、introduction to credit risk modelsPurpose of a credit risk modelCommon componentsModel from insurance (Credit Risk+)Credit MetricsKMVModel comparisonBank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 3BIS Regulatory Model Vs Credit Risk ModelsBIS Risk-Based

3、Capital RequirementsAll 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 O

4、ECD governments, banks, and securities dealers.Bank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 4Credit Risk Models- Credit Risk+- Credit Metrics- KMV- Other similar modelsBIS Regulatory Model Vs Credit Risk ModelsBank of ThailandRisk ManagemenBank of Thai

5、landRisk Management Symposium - September 2000Page 5Disadvantages 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

6、! BIS Regulatory Model Vs Credit Risk ModelsBank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 6BIS Regulatory Model Vs Credit Risk ModelsBig difference in probability of default exists across different credit qualities. Note: 1. Probability of default is ba

7、sed on 1-year horizon. 2. Historical statistics from Standard & Poors CreditWeek April 15, 1996.Bank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 7BIS Regulatory Model Vs Credit Risk ModelsDefault correlations can have significant impact on portfolio potent

8、ial 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 ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 8BIS Regulatory Mod

9、el 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 ThailandR

10、isk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 9Current Issues in Credit Risk ModellingAdapted from “Credit Risk Modelling: Current Practices and Applications”, April 1999, by Basle Committee on Banking SupervisionBank of ThailandRisk ManagemenBank of ThailandRisk Manage

11、ment Symposium - September 2000Page 10Current Issues in Credit Risk ModellingAdapted from “Credit Risk Modelling: Current Practices and Applications”, April 1999, by Basle Committee on Banking SupervisionBank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 11C

12、urrent Issues in Credit Risk ModellingAdapted from “Credit Risk Modelling: Current Practices and Applications”, April 1999, by Basle Committee on Banking SupervisionBank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 12Current Issues in Credit Risk ModellingA

13、dapted from “Credit Risk Modelling: Current Practices and Applications”, April 1999, by Basle Committee on Banking SupervisionBank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 13Credit Risk Models(A) Purpose of a credit risk modelMeasuring economic risk cau

14、sed byDefaultsDownratingsIdentifying risk sources and their contributionsScenario analysis and Stress testEconomic capital requirement and allocationPerformance evaluation (e.g. RAROC)Bank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 14Credit Risk Models(B)

15、 Common Components1. Model structureTransaction 1Transaction 2.Transaction 1Transaction 2.Counterparty ACounterparty BPortfolio of several counterparties and transactionsCorrelationsBank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 15Credit Risk Models2. Qu

16、antitative 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), Contrib

17、utory economic capital (CEC)Bank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 16Credit 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

18、rating upgrades/downgrades) are considered part of market risk.- Default probability is modeled as a continuous variable. Bank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 17Credit Risk Models(C) Model from Insurance (Credit Risk+)There are 3 types of uncer

19、tainty: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 ManagemenBank of ThailandRisk Management Symposium - September 2000Page 18Credit Risk Models(C) Model from Insurance (Credit Risk+)The whole

20、 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 ThailandRisk ManagemenBank of Thai

21、landRisk 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 ManagemenBank of ThailandRisk Management Symposium - September 2000Page 20Credit Risk Models(C) Model from Insurance

22、(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 ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 21Credit Risk

23、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 o

24、f ThailandRisk ManagemenBank of ThailandRisk Management 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

25、 defines scale of the distribution.Default intensityProbability densityBank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 23Credit Risk Models(C) Model from Insurance (Credit Risk+)Number of defaults (n)Default intensity ( )Bank of ThailandRisk ManagemenBank

26、 of ThailandRisk Management Symposium - September 2000Page 24Credit 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

27、(Over-dispersion)Bank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 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 Dist

28、ribution. # of defaultsProbability densityPoissonNegative BinomialEL(P) = EL(NGD)UL(P) UL(NGD)Bank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 26Credit Risk Models(C) Model from Insurance (Credit Risk+)The last source of uncertainty is the loss amount in c

29、ase 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 ThailandRisk ManagemenBank of ThailandRisk Management Symposium - Sept

30、ember 2000Page 27Credit Risk Models(C) Model from Insurance (Credit Risk+)Probability Distribution of Loss AmountBank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 28Credit Risk Models(C) Model from Insurance (Credit Risk+)Probability distribution of # of de

31、faultsProbability 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 ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 29Credit Risk M

32、odels(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 do

33、wngrades, and defaults.Bank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 30Credit 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 o

34、f uncertainty modeled here is the credit rating (or default) at which a particular counterparty will be one year from now.Bank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 31Credit Risk Models(D) Credit MetricsRatingTime01BBBBBBAAABDefaultBank of ThailandRi

35、sk ManagemenBank 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)Source: Standard & Poors CreditWeek April 15, 1996Bank of ThailandRisk ManagemenBank of

36、ThailandRisk Management Symposium - September 2000Page 33Credit Risk Models(D) Credit Metrics2. Spread matrix and recovery ratesSource: Carty & Lieberman (96a) -Moodys Investor ServiceBank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 34Credit Risk Models(D)

37、 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 ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 35Credit Risk M

38、odels(D) Credit MetricsLoss = Vcurrent - VnewEL, UL, Percentile, and VaR can be found. E(V)V(1st -percentile)VaRBank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 36Credit Risk Models(D) Credit MetricsIn the portfolio level, correlations are needed to combin

39、e 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

40、 of the “ability to pay”.Bank of ThailandRisk ManagemenBank 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

41、 each possible scenario:Probability that counterparty 1 and 2 will be rated BB and BBB respectivelyBank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 38Credit Risk Models(D) Credit MetricsSample Joint Transition Matrix(assuming 0.3 asset correlation)Source:

42、Credit Metrics- Technical Document, April 2, 1997, p. 38Bank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 39Credit Risk Models(D) Credit MetricsFor N counterparties, one way to find the loss distribution is to keep expanding the joint transition matrix. Thi

43、s, 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 Tha

44、ilandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 40Credit 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

45、 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 ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000P

46、age 41Credit Risk Models(D) Credit MetricsExposure DistributionRating migration likelihoodsSpread matrix and recovery ratesCorrelationsJoint credit rating changesPortfolio components and market volatilitiesValue and loss distribution of individual obligorsPortfolio value and loss distributionEL, UL,

47、 Percentile, and VaR can be found.SummaryBank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 42Credit 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 v

48、aries continuously with firm asset value and volatility.- Potentially a continuous credit migration.Bank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 43Credit Risk Models(E) “KMV-Type” ModelAnalysis is done on each individual counterparty, which will then b

49、e 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 ThailandRisk ManagemenBank of ThailandRisk Management Sym

50、posium - September 2000Page 44Credit Risk Models(E) “KMV-Type” ModelAbility to pay = Asset valueTime01Default point = Value of liabilitiesAsset value distributionDefault probabilityValueBank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 45Credit Risk Models(

51、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 ThailandRisk ManagemenBank

52、 of ThailandRisk Management Symposium - September 2000Page 46Credit 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 a

53、n option pricing model.Bank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 47Credit Risk Models(E) “KMV-Type” Model0Firm valueLiability value0Firm valueEquity valueBook value of liabilitiesBook value of liabilitiesLiabilities “Short put”Equity “Long call”Bank

54、 of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 48Credit 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 ThailandRisk ManagemenBank of ThailandRisk Management Sy

55、mposium - September 2000Page 49Credit 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 ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 200

56、0Page 50Credit 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 ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000P

57、age 51Credit 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

58、 reach the default point.- Correlation of default can, hence, be derived from correlation of asset value.Bank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 52Credit Risk Models(E) “KMV-Type” ModelFor 2 counterparties, the joint default probability can be calculated as follows:For a large number of counterparties, joint probabilities could become computationally difficult (the number of joint probabilities is 2N).Bank of ThailandRisk ManagemenBank of ThailandRisk Management Symposium - September 2000Page 53Credit Risk Mo