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Dynamic Hedging of Portfolio Credit Risk in a Markov Copula Model (Previous title: Dynamic Modeling of Portfolio Credit Risk with Common Shocks)

Author

Listed:
  • Bielecki, Tomasz R.

    (Illinois Institute of Technology and Université Lyon 1)

  • Cousin, Areski

    (Université d'Évry Val d'Essonne)

  • Crépey, Stéphane

    (Université d'Évry Val d'Essonne)

  • Herbertsson, Alexander

    (Department of Economics, School of Business, Economics and Law, Göteborg University)

Abstract

We consider a bottom-up Markovian copula model of portfolio credit risk where dependence among credit names mainly stems from the possibility of simultaneous defaults. Due to the Markovian copula nature of the model, calibration of marginals and dependence parameters can be performed separately using a two-steps procedure, much like in a standard static copula set-up. In addition, the model admits a common shocks interpretation, which is a very important feature as, thanks to it, efficient convolution recursion procedures are available for pricing and hedging CDO tranches, conditionally on any given state of the underlying multivariate Markov process. As a result this model allows us to dynamically hedge CDO tranches using single-name CDSs in a theoretically sound and practically convenient way. To illustrate this we calibrate the model against market data on CDO tranches and the underlying single-name CDSs. We then study the loss distributions as well as the min-variance hedging strategies in the calibrated portfolios.

Suggested Citation

  • Bielecki, Tomasz R. & Cousin, Areski & Crépey, Stéphane & Herbertsson, Alexander, 2011. "Dynamic Hedging of Portfolio Credit Risk in a Markov Copula Model (Previous title: Dynamic Modeling of Portfolio Credit Risk with Common Shocks)," Working Papers in Economics 502, University of Gothenburg, Department of Economics, revised 12 Oct 2012.
    • Handle: RePEc:hhs:gunwpe:0502
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    File URL: http://hdl.handle.net/2077/25503
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    References listed on IDEAS

    as
    1. Youssef Elouerkhaoui, 2007. "Pricing And Hedging In A Dynamic Credit Model," World Scientific Book Chapters, in: Alexander Lipton & Andrew Rennie (ed.), Credit Correlation Life After Copulas, chapter 6, pages 111-139, World Scientific Publishing Co. Pte. Ltd..
    2. Patton, Andrew J, 2001. "Modelling Time-Varying Exchange Rate Dependence Using the Conditional Copula," University of California at San Diego, Economics Working Paper Series qt01q7j1s2, Department of Economics, UC San Diego.
    3. Frey, Rüdiger & Backhaus, Jochen, 2010. "Dynamic hedging of synthetic CDO tranches with spread risk and default contagion," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 710-724, April.
    4. Alexander Herbertsson, 2011. "Modelling default contagion using multivariate phase-type distributions," Review of Derivatives Research, Springer, vol. 14(1), pages 1-36, April.
    5. Rama Cont & Yu Hang Kan, 2011. "Dynamic hedging of portfolio credit derivatives," Post-Print hal-00578008, HAL.
    6. Tomasz R. Bielecki & Igor Cialenco & Ismail Iyigunler, 2012. "Collateralized CVA Valuation with Rating Triggers and Credit Migrations," Papers 1205.6542, arXiv.org.
    7. Damiano Brigo & Andrea Pallavicini & Roberto Torresetti, 2007. "Cluster-Based Extension Of The Generalized Poisson Loss Dynamics And Consistency With Single Names," World Scientific Book Chapters, in: Alexander Lipton & Andrew Rennie (ed.), Credit Correlation Life After Copulas, chapter 2, pages 15-39, World Scientific Publishing Co. Pte. Ltd..
    8. Lindskog, Filip & McNeil, Alexander J., 2003. "Common Poisson Shock Models: Applications to Insurance and Credit Risk Modelling," ASTIN Bulletin, Cambridge University Press, vol. 33(2), pages 209-238, November.
    9. Bielecki, T.R. & Cousin, A. & Crépey, S. & Herbertsson, Alexander, 2012. "A Markov Copula Model of Portfolio Credit Risk with Stochastic Intensities and Random Recoveries," Working Papers in Economics 545, University of Gothenburg, Department of Economics.
    10. Youssef Elouerkhaoui, 2007. "Pricing And Hedging In A Dynamic Credit Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 703-731.
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    More about this item

    Keywords

    Portfolio Credit Risk; Basket Credit Derivatives; Dynamic Min-Variance Hedging; Common Shocks; Markov Copula Model;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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