A Generic One-Factor Lévy Model for Pricing Synthetic CDOs

  • Hansjörg Albrecher
  • Sophie A. Ladoucette
  • Wim Schoutens
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Summary

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 [12] used a one-factor Variance-Gamma (VG) model, Kalemanova et al. [7] and Guégan and Houdain [6] worked with a normal inverse Gaussian (NIG) factor model, and Baxter [3] 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.

Key words

Lévy processes collateralized debt obligation (CDO) credit risk credit default large homogeneous portfolio approximation 

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Copyright information

© Birkhäuser Boston 2007

Authors and Affiliations

  • Hansjörg Albrecher
    • 1
    • 2
  • Sophie A. Ladoucette
    • 3
  • Wim Schoutens
    • 3
  1. 1.Austrian Academy of SciencesJohann Radon InstituteAltenbergerstrasse 69Austria
  2. 2.Department of MathematicsGraz University of TechnologySteyrergasse 30Austria
  3. 3.Department of MathematicsKatholieke Universiteit LeuvenBelgium

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