Models Based on Copulas

One of the main risks in the management of large credit portfolios is inherent in the occurrence of disproportionately many joint defaults of different counterparties over a fixed time horizon. Hence it is essential to understand the impact of the default correlations and the dependence structure between the different obligors in the portfolio on the portfolio loss variable. [61] study dependent defaults in large credit portfolios based on both latent variable models as well as mixture models. In the CreditMetrics and the KMV model (representing the latent variable models) the joint default probabilities are assumed to follow a multivariate normal distribution. By this assumption large joint losses are assigned to low probabilities. Empirical evidence, however, shows that the joint default probability of extreme losses is actually larger than that induced by a multivariate normal dependence structure. Examples are the oil industry where 22 companies defaulted in 1982-1986 or the retail sector where over 20 defaults occurred in 1990-1992. Hence, assuming a normal distribution for portfolio losses, the probability of extreme losses can be underestimated. In order to reduce the model risk (the risk arising from a wrong specified model), [61] focus on the factors which have an impact on the tail of the loss distribution and, thus, also on the joint default probability as, for example, the default correlation and the individual default probabilities.