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Modelling Dependencies in Credit Risk Management

by Mark A. Nyfeler of the Swiss Federal Institute of Technology Zurich

November 23, 2000

Abstract: We commence with an overview of the three most widely used credit risk models developed by KMV, J.P. Morgan (CreditMetrics) and Credit Suisse First Boston (CreditRisk+). The mathematical essentials of each model lie in the way the joint distribution of the so-called 'default indicators' is modeled, a vector of Bernoulli random variables. With the focus on these vectors we investigate two general frameworks for modelling such binary random events. We also show how the KMV and CreditMetrics methodology can be translated into the framework of CreditRisk+. The credit risk models are then compared for 'homogeneous' portfolios using Monte Carlo simulation. As two of the three models use the multivariate normal distribution for their 'latent variables', we investigate the impact when proceeding to the broader class of elliptical distributions. A so-called t-model, incorporating a t-copula for the latent vector, is used to show the consequences of a possible generalisation. In this context we introduce the notion of tail dependence. Comparison of the extended t-model with the 'normal' two credit risk models is again performed for the same types of portfolios used for the previous comparison. Lastly, we study the portfolio loss distributions for the various models due to increased portfolio size.

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