The Computation Of The Loss Distribution Under The Framework Of CreditRisk+

In the past few decades, the credit risk management has been changing from traditional qualitative analysis to quantitative analysis and many major financial organizations haw introduced various credit risk management models in order to improve 1 he ability of controlling and forecasting the credit risk, such as KMV, CreditMetrics, CreditRisk+, CreditPortfolioView, etc. This paper focuses on expounding the CreditRisk+ model developed by Credit Suisse Financial Products (CSFP).In the technical documentation of CSFP, the loss distribution of a loan portfolio is derived by calculating the probability generating function(PGF) of the loss, and then using the Panjer Recursive method. Since then, some foreign scholars have proposed some new methods to compute the loss distributions, such as saddle-point approximation[2] by Gordy.M.B, a method combining Fast Fourier Transforms and Monte Carlo by Sandro Merino and Mark Nyfeler[19], which is referred as " FFT-Monte Carlo " in this paper, as well as FFT-Panjer method[20], which is proposed by K.K.Nazliben and K.Yildirak, etc.There is nearly no comprehensive exposition about the computing methods of the loss distribution on the existing articles, and even the FFT-Monte Carlo method isn't found in any Chinese literature. This paper will expound these methods one by one, and use an example and Matlab programes to help us to understand their principles and computing processes. One of the basic assumption of CreditRisk+ model is that the market factors follow Gamma distribution, considering that the Poisson-Gamma Mixture is Negative Binomial distribution, which makes the computation more simple. This paper will consider the situation that market factors are some other fat-tailed distributions(Inverse Gaussian distribution. Lognormal distribution, Pareto distribution). The loss's PGF in Inverse Gaussian distribution setting will be derived, and conclusion is obtained that the first three methods are not suitable for the computation of the loss distribution, but the FFT-Monte Carlo is an effective one. This is an innovatition of this paper.The main contents of this paper can be summarized as follows:Chapter I. Introduce the basic framework of CreditRisk+ model.Chapter II. Expound the four computation methods of the loss distribution, and an example and Matlab programes are also given.Chapter III. Analyze the loss distribution when the market factors follow other distribution with fatter tail.Chapter IV. Conclusions and suggestions.