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

by Olivier Le Courtois of EM Lyon, and
François Quittard-Pinon of the University of Lyon 1

November 22, 2006

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 an enhanced predictive power w.r.t. current Gaussian endogenous structural models.

JEL Classification: G32, G33.

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

Published in: Asia-Pacific Financial Markets, Vol. 13, No. 1, (March 2006), pp. 11-39.

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