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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. 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..
    2. Tomasz Bielecki & Stephane Crepey & Monique Jeanblanc, 2010. "Up and down credit risk," Quantitative Finance, Taylor & Francis Journals, vol. 10(10), pages 1137-1151.
    3. 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.
    4. 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.
    5. 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..
    6. 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.
    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.
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    Cited by:

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

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