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Dynamic Hedging of Portfolio Credit Risk in a Markov Copula Model

  • Tomasz R. Bielecki
  • Areski Cousin
  • Stéphane Crépey
  • Alexander Herbertsson
Article

Abstract

We devise a bottom-up dynamic model of portfolio credit risk where instantaneous contagion is represented by the possibility of simultaneous defaults. Due to a Markovian copula nature of the model, calibration of marginals and dependence parameters can be performed separately using a two-step procedure, much like in a standard static copula setup. In this sense this solves the bottom-up top-down puzzle which the CDO industry had been trying to do for a long time. This model can be used for any dynamic portfolio credit risk issue, such as dynamic hedging of CDOs by CDSs, or CVA computations on credit portfolios.

Keywords

Portfolio credit risk Credit derivatives Markov copula model Common shocks Dynamic hedging 

Notes

Acknowledgements

The research of T.R. Bielecki was supported by NSF Grant DMS–0604789 and NSF Grant DMS–0908099. The research of A. Cousin benefitted from the support of the DGE, the ANR project Ast&Risk and the “Chaire Management de la Modélisation”. The research of S. Crépey benefitted from the support of the “Chaire Risque de Crédit” and of the “Chaire Marchés en Mutation”, Fédération Bancaire Française. The research of A. Herbertsson was supported by the Jan Wallander and Tom Hedelius Foundation and by Vinnova.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Tomasz R. Bielecki
    • 1
  • Areski Cousin
    • 2
  • Stéphane Crépey
    • 3
  • Alexander Herbertsson
    • 4
  1. 1.Department of Applied MathematicsIllinois Institute of TechnologyChicagoUSA
  2. 2.Université de Lyon, Université Lyon 1LSAFLyonFrance
  3. 3.Laboratoire Analyse et ProbabilitésUniversité d’Évry Val d’EssonneÉvry CedexFrance
  4. 4.Center for finance/Department of EconomicsUniversity of GothenburgGothenburgSweden

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