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Dynamic Hedging of Portfolio Credit Risk in a Markov Copula Model

Author

Listed:
  • Tomasz R. Bielecki

    (Illinois Institute of Technology)

  • Areski Cousin

    (LSAF)

  • Stéphane Crépey

    (Université d’Évry Val d’Essonne)

  • Alexander Herbertsson

    (University of Gothenburg)

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.

Suggested Citation

  • Tomasz R. Bielecki & Areski Cousin & Stéphane Crépey & Alexander Herbertsson, 2014. "Dynamic Hedging of Portfolio Credit Risk in a Markov Copula Model," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 90-102, April.
    • Handle: RePEc:spr:joptap:v:161:y:2014:i:1:d:10.1007_s10957-013-0318-4
    DOI: 10.1007/s10957-013-0318-4
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    References listed on IDEAS

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    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. T. R. Bielecki & S. Crépey & M. Jeanblanc & B. Zargari, 2012. "Valuation And Hedging Of Cds Counterparty Exposure In A Markov Copula Model," World Scientific Book Chapters, in: Matheus R Grasselli & Lane P Hughston (ed.), Finance at Fields, chapter 4, pages 75-113, World Scientific Publishing Co. Pte. Ltd..
    3. 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..
    4. 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.
    5. Tomasz Bielecki & Stephane Crepey & Monique Jeanblanc, 2010. "Up and down credit risk," Quantitative Finance, Taylor & Francis Journals, vol. 10(10), pages 1137-1151.
    6. T. R. Bielecki & S. Crépey & M. Jeanblanc & B. Zargari, 2012. "Valuation And Hedging Of Cds Counterparty Exposure In A Markov Copula Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-39.
    7. 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.
    8. S. Crépey & M. Jeanblanc & D. Wu, 2013. "Informationally Dynamized Gaussian Copula," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(02), pages 1-29.
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    Cited by:

    1. Stéphane Crépey & Shiqi Song, 2018. "Counterparty risk and funding: immersion and beyond," Working Papers hal-01764403, HAL.
    2. Chamizo, Álvaro & Novales, Alfonso, 2021. "Evaluation of market risk associated with hedging a credit derivative portfolio," The Quarterly Review of Economics and Finance, Elsevier, vol. 80(C), pages 411-430.
    3. Yu-Sin Chang, 2018. "Systemic Risk and the Dependence Structures," Papers 1809.03425, arXiv.org.
    4. Herbertsson, Alexander, 2022. "Saddlepoint approximations for credit portfolios with stochastic recoveries," Working Papers in Economics 823, University of Gothenburg, Department of Economics.
    5. Stéphane Crépey & Shiqi Song, 2016. "Counterparty risk and funding: immersion and beyond," Finance and Stochastics, Springer, vol. 20(4), pages 901-930, October.
    6. Delia Coculescu & Gabriele Visentin, 2017. "A default system with overspilling contagion," Papers 1709.09255, arXiv.org, revised May 2023.

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