信用风险模型(共57页).ppt

1、Bank of ThailandPage 1Issues in Credit Risk ModellingRisk Management SymposiumSeptember 2, 2000Bank of ThailandChotibhak JotikasthiraBank of ThailandPage 2Overview BIS regulatory model Vs Credit risk models Current Issues in Credit Risk Modelling Brief introduction to credit risk models Purpose of a

2、 credit risk model Common components Model from insurance (Credit Risk+) Credit Metrics KMV Model comparisonBank of ThailandPage 3BIS Regulatory Model Vs Credit Risk ModelsBIS Risk-Based Capital RequirementsAll private-sector loans (uncollateralized) are subjected to an 8 percent capital reserve req

3、uirement, 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 ThailandPage 4Credit Risk Models- Credit Risk+- Credit Met

4、rics- KMV- Other similar modelsBIS Regulatory Model Vs Credit Risk ModelsBank of ThailandPage 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 potentiall

5、y result in too large a capital requirement! BIS Regulatory Model Vs Credit Risk ModelsBank of ThailandPage 6BIS Regulatory Model Vs Credit Risk ModelsBig difference in probability of default exists across different credit qualities. Credit Rating Probability of DefaultAAA0.00%AA0.00%A0.06%Credit Ra

6、ting Probability of DefaultBBB0.18%BB1.06%B5.20%CCC19.79%Note: 1. Probability of default is based on 1-year horizon. 2. Historical statistics from Standard & Poors CreditWeek April 15, 1996.Bank of ThailandPage 7BIS Regulatory Model Vs Credit Risk ModelsDefault correlations can have significant

7、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 ThailandPage 8BIS Regulatory Model Vs Credit Risk ModelsThe capital requiremen

8、t 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 ThailandPage 9Current Issues in Credit Risk ModellingAd

9、apted from “Credit Risk Modelling: Current 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 defa

10、ult mode and the mark-to-market mode models?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 cr

11、edit specific risks.Probability density functionNo 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

12、 UnconditionalCurrently, most models are unconditional (independent from the state of economy). Using these models, risk can understated or overstated depending on the location within the business cycle?Bank of ThailandPage 10Current Issues in Credit Risk ModellingAdapted from “Credit Risk Modelling

13、: Current Practices 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 t

14、o validate currently 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

15、 for bank credits. Most systems 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 ThailandPage 11Current Issues in Credit Risk

16、 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? Are the f

17、orward 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 a

18、re made to make different instruments comparable. The accuracy of estimates is questionable.Computational requirementSome models are computationally intensive.Bank of ThailandPage 12Current Issues in Credit Risk ModellingAdapted from “Credit Risk Modelling: Current Practices and Applications”, April

19、 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 testingStress testing should be u

20、sed 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 estimates of key parameters. Sensiti

21、vity analysis is, therefore, crucial in validating a model. Very limited work has been completed in this area to date.Bank of ThailandPage 13Credit Risk Models(A) Purpose of a credit risk model Measuring economic risk caused by Defaults Downratings Identifying risk sources and their contributions Sc

22、enario analysis and Stress test Economic capital requirement and allocation Performance evaluation (e.g. RAROC)Bank of ThailandPage 14Credit Risk Models(B) Common Components1. Model structureTransaction 1Transaction 2.Transaction 1Transaction 2.Counterparty ACounterparty BPortfolio of several counte

23、rparties and transactionsCorrelationsBank of ThailandPage 15Credit 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

24、 loss (UL), Portfolio risk- Economic capital (EC)- Risk contributions (RC), Contributory economic capital (CEC)Bank of ThailandPage 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 mo

25、vement and rating upgrades/downgrades) are considered part of market risk.- Default probability is modeled as a continuous variable. Bank of ThailandPage 17Credit Risk Models(C) Model from Insurance (Credit Risk+)There are 3 types of uncertainty:1. Actual number of defaults given a mean default inte

26、nsity2. Mean default intensity (only in the new approach!)3. Severity of loss Bank of ThailandPage 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 loa

27、ns to each class of borrowers can be viewed as a uniform portfolio.- m counterparties- a uniform default probability of p(m) Bank of ThailandPage 19Credit Risk Models(C) Model from Insurance (Credit Risk+)DPCounterpartiesm1, p(m1)m2, p(m2)m3, p(m3)m4, p(m4)Bank of ThailandPage 20Credit Risk Models(C

28、) Model 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 ThailandPage 21Credit Risk Models(C) Model from Insurance (Cre

29、dit 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 ThailandPage 22Credit Risk Models

30、(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 ThailandPage 23Credit Ris

31、k Models(C) Model from Insurance (Credit Risk+)Number of defaults (n)Default intensity ( ),()(Poissonn),(nomialNegativeBinBank of ThailandPage 24Credit Risk Models(C) Model from Insurance (Credit Risk+)Defaults are now related since they are exposed to the same default intensity. Higher default inte

32、nsity effects all obligors in the portfolio.First moment:Second moment:)(nE)1 ()(nVMean Variance(Over-dispersion)Bank of ThailandPage 25Credit Risk Models(C) Model from Insurance (Credit Risk+)Negative Binomial Distribution (NGD) exhibits over-dispersion and “fatter tails”, which make it closer to r

33、eality than Poisson Distribution. # of defaultsProbability densityPoissonNegative BinomialEL(P) = EL(NGD)UL(P) UL(NGD)Bank of ThailandPage 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 bucke

34、ting 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 ThailandPage 27Credit Risk Models(C) Model from Insurance (Credit Risk+)0%10%20%30%40%50%Under 5050 to 100100 to 200Ov

35、er 200Loss amountProbabilityProbability Distribution of Loss AmountBank of ThailandPage 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 amoun

36、tThe analytic formula of the loss distribution in the form of probability generating function (PGF)Probability, EL, UL, and Percentile can be found.Bank of ThailandPage 29Credit Risk Models(D) Credit Metrics- Introduced in 1997 by J.P. Morgan.- Both defaults and spread changes due to rating upgrades

37、/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 ThailandPage 30Credit Risk Models(D) Credit MetricsAnalysis is done on each individua

38、l 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 ThailandPage 31Credit Risk Models(D) Credit MetricsRatingT

39、ime01BBBBBBAAABDefaultBank of ThailandPage 32Credit Risk Models(D) Credit MetricsIn the counterparty level, two inputs are required:1. Credit transition matrix (Moodys, S&P or KMV)InitialRatingAAAAAABBBBBBCCCDAAA90.818.330.680.060.12000AA0.790.657.790.640.060.140.020A0.092.2791.055.520.740.260.0

40、10.06BBB0.020.335.9586.920.18BB0.030.140.677.7380.538.8411.06B036.4883.644.075.2CCC0.2811.2464.8619.79Rating at Year-End (%)Source: Standard & Poors CreditWeek April 15, 1996Bank of ThailandPage 33Credit Risk Models(D) Credit Metrics2. Spread matrix and recovery

41、 ratesSource: Carty & Lieberman (96a) -Moodys Investor ServiceCreditCreditRatingSpreadAAASAAAAASAAASABBBSBBBBBSBBBSBCCCSCCCMean (%) STD (%)Senior secured53.826.86Senior unsecured51.1325.45Senior subordinated38.5223.81Subordinated32.7420.18Junior subordinated17.0910.9Seniority ClassRecovery RateB

42、ank of ThailandPage 34Credit Risk Models(D) Credit MetricsPossible values of loan one year from now can then be calculated, each of which has its own probability:CreditInterestLoanProbabailityRatingRateValue(%)AAARf + SAAA1100.02AARf + SAA1090.33ARf + SA1085.95BBBRf + SBBB10786.93BBRf + SBB1025.3BRf

43、 + SB981.17CCCRf + SCCC840.12Default1 - RR510.18Now, the loan is rated BBB. Its bond equivalent yield is Rf + SBBB.1 yearBank of ThailandPage 35Credit Risk Models(D) Credit Metrics0204060801006080100120Loan valueProbability (%)Loss = Vcurrent - VnewEL, UL, Percentile, and VaR can be found. E(V)V(1st

44、 -percentile)VaRBank of ThailandPage 36Credit 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 (lowe

45、r 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 ThailandPage 37Credit Risk Models(D) Credit MetricsIn order to find the loss distribution of a 2-counterparty portfolio, we need to cal

46、culate the joint migration probabilities and the payoffs for each possible scenario:BBZBZAZBBBZABBBBBBdrdrrrfZrZZrZP212121);,(),(Probability that counterparty 1 and 2 will be rated BB and BBB respectivelyBank of ThailandPage 38Credit Risk Models(D) Credit MetricsAAAAAABBBBBBCCCDefault0.092.2791.055.

47、520.740.260.010.06AAA0.020.000.000.020.000.000.000.000.00AA0.330.000.040.290.000.000.000.000.00A5.950.020.395.440.080.010.000.000.00BBB86.930.071.8176.694.550.570.190.010.04BB5.300.000.024.470.640.110.040.000.01B1.170.000.000.920.180.040.020.000.00CCC0.120.000.000.090.020.000.000.000.00Default0.180.

48、000.000.130.040.010.000.000.00Obligor#2 (A)Obligor#1(BBB)Sample Joint Transition Matrix(assuming 0.3 asset correlation)Source: Credit Metrics- Technical Document, April 2, 1997, p. 38Bank of ThailandPage 39Credit Risk Models(D) Credit MetricsFor N counterparties, one way to find the loss distributio

49、n 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

50、loss distributions that are close to normal.Bank of ThailandPage 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 portfolio method

51、ology 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 ThailandPage 41Credit Risk Models(D) Credit MetricsExposure DistributionRating migration likelihoo

52、dsSpread matrix and recovery ratesCorrelationsJoint 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 ThailandPage 42Credit Risk Models(E) “KM

53、V-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 ThailandPage 43Credit Risk Models(E) “KMV-Type” Model

54、Analysis 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

55、. Bank of ThailandPage 44Credit Risk Models(E) “KMV-Type” ModelAbility to pay = Asset valueTime01Default point = Value of liabilitiesAsset value distributionDefault probabilityValueBank of ThailandPage 45Credit Risk Models(E) “KMV-Type” ModelThe question is “how to find the distribution of future as

56、set 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 ThailandPage 46Credit Risk Models(E) “KMV-Type” ModelSince we can observe only equity value and its vol

57、atility, 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 ThailandPage 47Credit Risk Models(E) “KMV-Type” Model0Firm valueLiability value0Firm valueEquity valueBook value of li

58、abilitiesBook value of liabilitiesLiabilities “Short put”Equity “Long call”Bank of ThailandPage 48Credit Risk Models(E) “KMV-Type” ModelEquity is like a call option on the firm asset:),.,(othersVfVAAcallE),/,(DeltaEDVfAAvolatilityETwo unknowns ( and ) can be solved from these two equations.AVABank o

59、f ThailandPage 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.AADefaultPoVEDDint)(1Bank of ThailandPage 50Credit Risk Models(E) “KMV-Type” ModelKMV claims that for

60、 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 ThailandPage 51Credit Risk Models(E) “KMV-Type” ModelLike Credit Metrics, correlations are needed to combine all counterparties (or loans) into a portfolio and f