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Tails of Credit Default Portfolios

by Gabriel Kuhn of the Munich University of Technology

December 21, 2004

Abstract: We derive analytic expressions for the tail behavior of credit losses in a large homogeneous credit default portfolio. Our model is an extended CreditMetrics model; i.e. it is a one-factor model with a multiplicative shock-variable. We show that the first order tail behavior is robust with respect to this shock-variable. In a simulation study we compare different models for the latent variables. We fix default probability and correlation of the latent variables and the first order tail behavior of the limiting credit losses in all models and observe a completely different tail behavior leading to very different VaR estimates. For three portfolios of different credit quality we suggest a pragmatic model selection procedure and compare the fit with that of the β-model.

JEL Classification: G11, G21, G39, C19.

AMS Classification: 91B28, 60F05, 91B70, 62E20, 60B10.

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