Risk-Neutral and Actual Default Probabilities with an Endogenous Bankruptcy Jump-Diffusion Model

Abstract

This paper focuses on historical and risk-neutral default probabilities in a structural model, when the firm assets dynamics are modeled by a double exponential jump diffusion process. Relying on the Leland [1994a, 1994b] or Leland and Toft [1996] endogenous structural approaches, as formalized by Hilberink and Rogers [2002], this article gives a coherent construction of historical default probabilities. The risk-neutral world where evolve the firm assets, modeled by a geometric Kou process, is constructed based on the Esscher measure, yielding useful and new analytical relations between historical and risk-neutral probabilities. We do a complete numerical analysis of the predictions of our framework, and compare these predictions with actual data. In particular, this new framework displays a greater predictive power than current Gaussian endogenous structural models.

Keywords: Cumulative Default Probability, Structural Model, Jump-Diffusion, Endogenous Capital Structure, Esscher Transform, Kou Processes

JEL Classification: G32, G33