Encyclopedia of Financial Models I

Default Correlation in Intensity Models for Credit Risk Modeling

ABEL ELIZALDE, PhD

Credit Derivatives Strategy, J.P. Morgan

Abstract: The two primary types of credit risk models that seek to statistically describe default processes are the reduced-form model and the structural model. The most extended types of reduced-form models are the intensity models. There are three main approaches to incorporate credit risk correlation among firms within the framework of reduced models. The first approach, the conditionally independent defaults models, introduces credit risk dependence among firms through the dependence of the firms’ default intensity processes on a common set of state variables. Contagion models extend the conditionally independent defaults 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.

There are two primary types of models in the literature that attempt to describe default processes for debt obligations and other defaultable financial instruments, usually referred to as structural and reduced-form (or intensity) models.

Structural models use the evolution of firms’ structural variables, such ...