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Counterparty Risk on a CDS in a Markov Chain Copula Model with Joint Defaults

In: Recent Advances In Financial Engineering 2009

Author

Listed:
  • S. Crépey

    (Équipe Analyse et Probabilité, Université d'Évry Val d'Essonne, Bd. F. Mitterrand, 91025 Évry Cedex, France and http://www.cris-creditrisk.com CRIS Consortium, France)

  • M. Jeanblanc

    (Équipe Analyse et Probabilité, Université d'Évry Val d'Essonne, Bd. F. Mitterrand, 91025 Évry Cedex, France and http://www.cris-creditrisk.com CRIS Consortium, France)

  • B. Zargari

    (Équipe Analyse et Probabilité, Université d'Évry Val d'Essonne, Bd. F. Mitterrand, 91025 Évry Cedex, France and Dept. of Mathematical Sciences, Sharif University of Technology, Azadi Ave., PO Box: 11365-11155, Tehran, Iran)

Abstract

In this paper we study the counterparty risk on a payer CDS in a Markov chain model of two reference credits, the firm underlying the CDS and the protection seller in the CDS. We first state few preliminary results about pricing and CVA of a CDS with counterparty risk in a general set-up. We then introduce a Markov chain copula model in which wrong way risk is represented by the possibility of joint defaults between the counterpart and the firm underlying the CDS. In the set-up thus specified we derive semi-explicit formulas for most quantities of interest with regard to CDS counterparty risk such as price, CVA, EPE or hedging strategies. Model calibration is made simple by the copula property of the model. Numerical results show adequacy of the behavior of EPE and CVA in the model with stylized features.

Suggested Citation

  • S. Crépey & M. Jeanblanc & B. Zargari, 2010. "Counterparty Risk on a CDS in a Markov Chain Copula Model with Joint Defaults," World Scientific Book Chapters, in: Masaaki Kijima & Chiaki Hara & Keiichi Tanaka & Yukio Muromachi (ed.), Recent Advances In Financial Engineering 2009, chapter 4, pages 91-126, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789814304078_0004
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    Citations

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    Cited by:

    1. Harb, Etienne & Louhichi, Wael, 2017. "Pricing CDS spreads with Credit Valuation Adjustment using a mixture copula," Research in International Business and Finance, Elsevier, vol. 39(PB), pages 963-975.
    2. Weijie Pang & Stephan Sturm, 2020. "XVA Valuation under Market Illiquidity," Papers 2011.03543, arXiv.org.
    3. Bo, Lijun & Capponi, Agostino, 2015. "Counterparty risk for CDS: Default clustering effects," Journal of Banking & Finance, Elsevier, vol. 52(C), pages 29-42.
    4. Cyril Durand & Marek Rutkowski, 2013. "CVA for Bilateral Counterparty Risk under Alternative Settlement Conventions," Papers 1307.6486, arXiv.org.

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