tailieunhanh - Dependent Defaults in Models of Portfolio Credit Risk

We analyse 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. | Dependent Defaults in Models of Portfolio Credit Risk Rudiger Frey Department of Mathematics University of Leipzig Augustusplatz 10 11 D-04109 Leipzig frey@ Alexander J. McNeil Department of Mathematics Federal Institute of Technology ETH Zentrum CH-8092 Zurich mcneil@ 16th June 2003 Abstract We analyse 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. . Subject Classification G31 G11 C15 Keywords Risk Management Credit Risk Dependence Modelling Copulas 1 Introduction A major cause of concern in managing the credit risk in the lending portfolio of a typical financial institution is the occurrence of disproportionately many joint defaults of different counterparties over a fixed time horizon. Joint default events also have an an important impact on the performance of derivative securities whose payoff is linked to the loss of a whole portfolio of underlying bonds or loans such as collaterized debt obligations CBOs CDOs CLOs or basket credit derivatives. In fact the occurrence of disproportionately many joint defaults is what