1、Ri$kLab.CNTMM,Slide1,Quantitative Risk Management- Credit Risk Modelling,Ming-Heng ZhangRi$kLab.CN,Ri$kLab.CNTM,Slide2,Credit risk is the risk that the value of the portfolio changes due to unexpected changes in the credit quality of issues or trading partners.,Whats Credit Risk?,Ri$kLab.CNTM,Slide3
2、,Introduction,Credit risk modelThere are two main areas of application for quantitative risk models: credit risk management and the analysis of credit-risk securities.Credit risk management models are used to determine the loss distribution of a loan or bond portfolio over a fixed time period, and t
3、o compute the loss measure or to make risk capital allocations .Credit risk securities, dynamic models, because the payoff of most products depends on the exact timing of default .,Ri$kLab.CNTM,Slide4,Challenging,Challenging Lack of public information and data Skew loss distribution The role of depe
4、ndence modeling,Ri$kLab.CNTM,Slide5,Structural Model of Default,Assumptions (The Merton model 1974)Firms asset value follows some stochastic process, the firm finance itself by equity and by debt , cannot pay out dividends or issue new debt. Default occurs if the firm misses a payment to its debt ho
5、lders at the end of the maturity;Frictionless markets with continuous trading;The risk-free interest rate is deterministic and equal to r0;The firms asset value process is independent of the way the firm is financed, and in particular it is independent of the debt level, moreover assets is tradable
6、security.,Ri$kLab.CNTM,Slide6,The Merton Model,Ri$kLab.CNTM,Slide7,Pricing in Merton Model,General pricing result Consider a claim on the value of the firm with maturity T and payoff h(Vt ).Two ways to compute the fair value f(t ,Vt )PDE (partial differential equation)Risk neutral pricing approach,R
7、i$kLab.CNTM,Slide8,Application,Ri$kLab.CNTM,Slide9,Credit Risk Spread,The credit spread measure the difference of the continuously compounded yield to maturity of a default free zero coupon bound and of a default able zero coupon bond,Ri$kLab.CNTM,Slide10,Extension,Firms can default at any time Endo
8、genous default threshold Stochastic rate,Ri$kLab.CNTM,Slide11,The KMV model,The key quantity of interest in the KMV model is the so called EDF (expected default frequency):Moreover ,KMV does not assume that the asset value V 0 of the firm is directly observable,Ri$kLab.CNTM,Slide12,Models based on c
9、redit migration,Developed by JP Morgan and the RiskMetrics group 1997Specify the probability of moving from one credit rating to another credit rating over the given risk horizon Example : credit migration process follows a time homogeneous Markov chain (the hypothesis has been criticized heavily on
10、 empirical grounds )(pay attention to the comments about KMV),Ri$kLab.CNTM,Slide13,Threshold Models,Ri$kLab.CNTM,Slide14,The Mixture Model Approach,Bernoulli mixture modelPoisson mixture modelCreditRisk+Asymptotic for large portfolioThreshold models as mixture models,Ri$kLab.CNTM,Slide15,Monte Carlo
11、 Methods,Compute expected shortfall and expected shortfall contributions at the confidence level for our portfolioEvaluate the conditional expectationsThere is a variancereduction technique known as Importance Sampling Basics of Importance Sampling,Ri$kLab.CNTM,Slide16,Inferring,MotivationsThe calib
12、ration of portfolio credit risk models used in industry has not relies on the formal statistical estimation of model parameters from historical default and migration data;For there are simply not enough relevant data on historical defaults to obtain reliable parameter estimates by formal inference a
13、lone;Question is that how much confidence can be placed in the model parameters thus derived, and how model risk remains?,Ri$kLab.CNTM,Slide17,Models and Notes,Exchangeable BernoulliMixture ModelsMixture Models as GlMMsNotes and CommentsOnly describe default models it is also possible to analysis ra
14、ting migrations in the generalized linear model framework, as the ordered probit model.A further extend to rating transition data with Markov chain models;Latent structure to capture the dynamics of systematic Risk.,Ri$kLab.CNTM,Slide18,Refs,M.Ammann, Credit Risk Valuation Methods, Models, and Application, 2nd, SpringerA.J.McNeil, R.Frey and P.Embrechts, 2005, Quantitative Risk Management Concepts, Techniques and Tools, Princeton PressP.Embrechts, C.Kluppelberg and T.Mikosch, 1997, Modelling Extremal Events for Insurance and Finance, Springer-Verlag,Ri$kLab.CNTM,Slide19,End of ,
