Tails of Credit Default Portfolios

Kuhn, Gabriel (2005): Tails of Credit Default Portfolios. Collaborative Research Center 386, Discussion Paper 410

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 modelsand 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 beta-model.

• Item Type: Paper (Research Paper)
• Keywords: beta-model, credit default portfolio, extreme value theory, heavy-tailed risk factor, latent variable model, multivariate t-distribution, one factor model, regular variation, tail behavior of portfolio credit loss, Value at Risk (VaR)
• Subjects: Mathematics, Computer Science and Statistics; Mathematics, Computer Science and Statistics > Statistics; Mathematics, Computer Science and Statistics > Statistics > Collaborative Research Center 386
• Dewey Classification: 600 Natural sciences and mathematics; 600 Natural sciences and mathematics > 510 Mathematics