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A generic one-factor Levy model for pricing synthetic CDOs
Title of the book
Advances in Mathematical Finance
Address of publication
Fu M., Jarrow R., Yen J., Elliott R. J.
Applied and Numerical Harmonic Analysis
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 Guégan 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.
Lévy processes, collateralized debt obligation (CDO), credit risk, credit default, large homogeneous portfolio approximation
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