ABSTRACT

We analyze the mathematical structure of portfolio credit risk models with particular regard to the modelling of dependence between default events in these models. We explore the role of copulas in latent variable models (the approach that underlies KMV and CreditMetrics) and use non-Gaussian copulas to present extensions to standard industry models. We explore the role of the mixing distribution in Bernoulli mixture models (the approach underlying CreditRisk+) and derive large portfolio approximations for the loss distribution. We show that all currently used latent variable models can be mapped into equivalent mixture models, which facilitates their simulation, statistical fitting and the study of their large portfolio properties. Finally we develop and test several approaches to model calibration based on the Bernoulli mixture representation; we find that maximum likelihood estimation of parametric mixture models generally outperforms simple moment estimation methods.