Modelling Dependent Defaults
August 13, 2001
Abstract: We consider the modelling of dependent defaults in large credit portfolios using latent variable models (the approach that underlies KMV and CreditMetrics) and mixture models (the approach underlying CreditRisk+). We explore the role of copulas in the latent variable framework and show that for given default probabilities of individual obligors the distribution of the number of defaults in the portfolio is completely determined by the copula of the latent variables. We present results from a simulation study showing that, even for fixed asset correlations, assumptions concerning the latent variable copula can have a profound effect on the distribution of credit losses. In the mixture models defaults are conditionally independent given a set of common economic factors affecting all obligors and we explore the role of the mixing distribution of the factors in these models. In homogeneous, one-factor mixture models we find that the tail of the mixing distribution essentially determines the tail of the overall credit loss distribution. We discuss the relationship between latent variable models and mixture models and provide general conditions under which these models can be mapped into each other. Our contribution can be viewed as an analysis of the model risk associated with the modelling of dependence between individual default events.
Keywords: Portfolio Credit Risk Models, Model Risk, Dependence Modelling, Copulas, Mixture Models.
See also a closely related paper:
Modelling Dependent Defaults: Asset Correlations Are Not Enough!
March 9, 2001
Introduction: In this article we focus on the latent variable approach to modelling credit portfolio losses. This methodology underlies all models that descend from Merton firm-value model (Merton 1974). In particular, it underlies the most important industry models, such as the model proposed by the KMV corporation and CreditMetrics.