信用风险模型ppt课件

1、Issues in Credit Risk ModellingRisk Management SymposiumSeptember 2, 2000Bank of ThailandChotibhak Jotikasthira.OverviewBIS regulatory model Vs Credit risk modelsCurrent Issues in Credit Risk ModellingBrief introduction to credit risk modelsPurpose of a credit risk modelCommon componentsModel from i

2、nsurance (Credit Risk+)Credit MetricsKMVModel comparison.BIS Regulatory Model Vs Credit Risk ModelsBIS Risk-Based 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 cre

3、dit quality of the borrowing counterparty. Note: Some adjustments are made to collateralized/guaranteed loans to OECD governments, banks, and securities dealers.Credit Risk Models- Credit Risk+- Credit Metrics- KMV- Other similar modelsBIS Regulatory Model Vs Credit Risk Models.Disadvantages of BIS

4、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 Models.BIS Regulatory Model Vs Cred

5、it 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.BIS Regulatory Model Vs Credit Risk ModelsDefault correlations can hav

6、e 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.BIS Regulatory Model Vs Credit Risk ModelsThe capital requirement to cov

7、er 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.Current Issues in Credit Risk ModellingAdapted from “Credit Risk Modell

8、ing: Current Practices and Applications, April 1999, by Basle Committee on Banking Supervision.Current Issues in Credit Risk ModellingAdapted from “Credit Risk Modelling: Current Practices and Applications, April 1999, by Basle Committee on Banking Supervision.Current Issues in Credit Risk Modelling

9、Adapted from “Credit Risk Modelling: Current Practices and Applications, April 1999, by Basle Committee on Banking Supervision.Current Issues in Credit Risk ModellingAdapted from “Credit Risk Modelling: Current Practices and Applications, April 1999, by Basle Committee on Banking Supervision.Credit

10、Risk Models(A) Purpose 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).Credit Risk Models(B) Common Components1. M

11、odel structureTransaction 1Transaction 2.Transaction 1Transaction 2.Counterparty ACounterparty BPortfolio of several counterparties and transactionsCorrelations.Credit Risk Models2. Quantitative variables/parameters- Default probability/intensity (PD, EDF)- Loan equivalent exposure (LEE)- Loss given

12、 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).Credit Risk Models(C) Model from Insurance (Credit Risk+)- Only two states of the world

13、 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. .Credit Risk Models(C) Model from Insurance (Credit Risk+)There are 3 types of uncertain

14、ty:1. Actual number of defaults given a mean default intensity2. Mean default intensity (only in the new approach!)3. Severity of loss .Credit 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 defa

15、ult 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) .Credit Risk Models(C) Model from Insurance (Credit Risk+)DPCounterpartiesm1, p(m1)m2, p(m2)m3, p(m3)m4, p(m4).Credit Risk Models(C) Model f

16、rom 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 year.Credit Risk Models(C) Model from Insurance (Credit Risk+)If default intensity ( ) is constan

17、t, 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).Credit Risk Models(C) Model from Insurance (Credit Risk+)The new approach incorporates

18、 dependency of counterparties by assuming that default intensity is random and follows gamma distribution. defines shape, and defines scale of the distribution.Default intensityProbability density.Credit Risk Models(C) Model from Insurance (Credit Risk+)Number of defaults (n)Default intensity ( ).Cr

19、edit 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).Credit Risk Models(C) Model from Insurance (C

20、redit 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).Credit Risk Models(C) Model from Insurance (Credit Risk+)The la

21、st 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.Credit Risk Models(C) Model fr

22、om Insurance (Credit Risk+)Probability Distribution of Loss Amount.Credit 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 (PG

23、F)Probability, EL, UL, and Percentile can be found.Credit 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 credi

24、t rating have the same probability of rating upgrades, rating downgrades, and defaults.Credit 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 t

25、he credit rating (or default) at which a particular counterparty will be one year from now.Credit Risk Models(D) Credit MetricsRatingTime01BBBBBBAAABDefault.Credit Risk Models(D) Credit MetricsIn the counterparty level, two inputs are required:1. Credit transition matrix (Moodys, S&P or KMV)Source:

26、Standard & Poors CreditWeek April 15, 1996.Credit Risk Models(D) Credit Metrics2. Spread matrix and recovery ratesSource: Carty & Lieberman (96a) -Moodys Investor Service.Credit Risk Models(D) Credit MetricsPossible values of loan one year from now can then be calculated, each of which has its own p

27、robability:Now, the loan is rated BBB. Its bond equivalent yield is Rf + SBBB.1 year.Credit Risk Models(D) Credit MetricsLoss = Vcurrent - VnewEL, UL, Percentile, and VaR can be found. E(V)V(1st -percentile)VaR.Credit Risk Models(D) Credit MetricsIn the portfolio level, correlations are needed to co

28、mbine 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 correlati

29、on of the “ability to pay.Credit 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 respect

30、ively.Credit Risk Models(D) Credit MetricsSample Joint Transition Matrix(assuming 0.3 asset correlation)Source: Credit Metrics- Technical Document, April 2, 1997, p. 38.Credit Risk Models(D) Credit MetricsFor N counterparties, one way to find the loss distribution is to keep expanding the joint tran

31、sition 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

32、normal.Credit 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 con

33、tribution (RC) for individual counterparties. RC is useful in identifying the counterparties to which we have excessive risk exposure.Credit Risk Models(D) Credit MetricsExposure DistributionRating migration likelihoodsSpread matrix and recovery ratesCorrelationsJoint credit rating changesPortfolio

34、components and market volatilitiesValue and loss distribution of individual obligorsPortfolio value and loss distributionEL, UL, Percentile, and VaR can be found.Summary.Credit Risk Models(E) “KMV-Type Model- One or both defaults and spread changes due to rating upgrades/downgrades can be incorporat

35、ed.- EDF is firm-specific.- EDF varies continuously with firm asset value and volatility.- Potentially a continuous credit migration.Credit Risk Models(E) “KMV-Type ModelAnalysis is done on each individual counterparty, which will then be combined into a portfolio, using asset-value correlations. Th

36、erefore, 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. .Credit Risk Models(E) “KMV-Type ModelAbility to pay = Asset valueTime01Default point = Value of liabilitiesAsset value distribu

37、tionDefault probabilityValue.Credit 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 v

38、olatility. .Credit 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.Credit Risk Models(E) “KMV-

39、Type Model0Firm valueLiability value0Firm valueEquity valueBook value of liabilitiesBook value of liabilitiesLiabilities “Short putEquity “Long call.Credit 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.Credit

40、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.Credit Risk Models(E) “KMV-Type ModelKMV claims that for a given DD, EDF is remarkably constant across key variables:- Industr

41、y/sector- Company size- TimeThis provides a robust basis for DD-EDF mapping.Credit 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 fi

42、rm asset- EDF is defined as a chance that the “ability to pay will reach the default point.- Correlation of default can, hence, be derived from correlation of asset value.Credit 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).Credit Risk Models(E) “KMV-Type ModelWhen the loss distribution is close to normal, th