A Generic One Factor Lévy Model for Pricing Synthetic CDOs

by Hansjörg Albrecher of the Radon Institute, Austrian Academy of Sciences, Linz & Graz University of Tech.
Sophie A. Ladoucette of Katholieke Universiteit Leuven, and
Wim Schoutens of Katholieke Universiteit Leuven

September 2006

Abstract: The one-factor Gaussian model is well known not to fit the prices of the different tranches of a collateralized debt obligation (CDO) simultaneously, leading to the implied correlation smile. Recently, other one-factor models based on different distributions have been proposed. Moosbrucker used a one-factor Variance Gamma (VG) model, Kalemanova et al. and Guegan and Houdain worked with a normal inverse Gaussian (NIG) factor model, and Baxter introduced the Brownian variance-gamma (BVG) model. These models bring more flexibility into the dependence structure and allow tail dependence. We unify these approaches, describe a generic one-factor Lévy model, and work out the large homogeneous portfolio (LHP) approximation. Then we discuss several examples and calibrate a battery of models to market data.

JEL Classification: C60.

Keywords: Lévy processes; collateralized debt obligation (CDO); credit risk; credit default; large homogeneous portfolio approximation.

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