Semi-Analytical Valuation of Basket Credit Derivatives in Intensity-Based Models

Abstract

Credit risk models today mostly come from two different families: structural models and reduced-form, or intensity-based, models. In the former, default probabilities are derived from estimates of how far a given firm's net asset value is above a critical level at which it would default. Default correlations come from correlation in the underlying firm values. In intensity-based models, default is modeled as the first jump in a pure jump process, with a jump intensity that may be a function of exogenous factors. Default correlation arises from correlation in those factors. The expanding market for “correlation products,” such as basket credit derivatives, raises the need to deal explicitly with default correlation; so far, there has been relatively greater emphasis on the structural approach exemplified by the Gaussian copula model. In this article, Mortensen argues that an intensity-based approach can work just as well, or better. He presents a general model in which default intensities are driven by affine jump-diffusion processes, with a common factor that produces correlation among issuers, and one independent idiosyncratic factor per issuer. Calibrating against tranche prices from CDX and iTraxx CDOs, the intensity-based model is shown to be capable of fitting the market better than standard copula methods.