Tail approximation for credit risk portfolios with heavy-tailed risk factors

Abstract

We consider a portfolio credit risk model in the spirit of CreditMetrics [15]. The multivariate normally distributed underlying risk factors in that model are replaced by more general multivariate elliptical factors with heavy-tailed marginals, introducing tail-dependence. We consider a full-scale version of the model, i.e. we incorporate not only the default risk, but also rating migrations, credit spread volatility and recovery risk. We derive an upper bound of the portfolio loss distribution, which is particularly accurate at high loss levels. Given the complexity of our model, we obtain this results using a mixture of analytic techniques and Monte Carlo simulation. We conclude with an approximation of VaR and a new method to determine the contributions of the individual credits to the overall portfolio risk. ∗GKAAM, Munich University of Technology, D-85747 Garching, Germany, tel:(++49)(+89)28917991, email: krassi@ma.tum.de, http://www.ma.tum.de/stat The author is supported financially by a scholarship from DFG (Deutsche Forschungsgemeinschaft) through Graduate Program Applied Algorithmic Mathematics AMS 2000 Mathematics Subject Classification: 62H99, 65C20, 91B28 JEL Classification: G11, G21