Credit Risk Models I: Default Correlation in Intensity Models

This report analyzes reduced-form credit risk models, and reviews the three main approaches to incorporate credit risk correlation among firms within the framework of reduced models. The first approach, conditionally independent defaults (CID) models, introduces credit risk dependence of the firms’ default intensity processes on a common set of state variables. Contagion models extend the CID approach to account for default clustering (periods in which the firms’ credit risk is increased and in which the majority of the defaults take place). Finally, default dependencies can also be accounted for using copula functions. The copula approach takes as given the marginal default probabilities of the different firms and plugs them into a copula function, which provides the model with the default dependence structure. After a description of copulas, we present two different approaches of using copula functions in intensity models, and discuss the choice and calibration of the copula function.