A Direct Approach to Arbitrage-Free Pricing of Credit Derivatives1

Abstract

This paper develops a framework for modelling risky debt and valuing credit derivatives that is exible and simple to implement, and that is, to the maximum extent possible, based on observables. Our approach is based on expanding the Heath-Jarrow-Morton term-structure model to allow for defaultable debt. We do not follow the procedure of implying out the behavior of spreads from assumptions concerning the default process, instead working directly with the evolution of spreads. We show that risk-neutral drifts in the resulting model possess a recursive representation that particularly facilitates implementation and makes it possible to handle path-dependence and early exercise features without difficulty. The framework permits embedding a variety of specifications for default; we present an empirical example of a default structure which provides promising calibration results.