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Unilateral CVA for CDS in Contagion Model_with Volatilities and Correlation of Spread and Interest

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  • Bao, Qunfang
  • Chen, Si
  • Liu, Guimei
  • Li, Shenghong
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    Abstract

    The price of financial derivative with unilateral counterparty credit risk can be expressed as the price of an otherwise risk-free derivative minus a credit value adjustment(CVA) component that can be seen as shorting a call option, which is exercised upon default of counterparty, on MtM of the derivative. Therefore, modeling volatility of MtM and default time of counterparty is key to quantification of counterparty risk. This paper models default times of counterparty and reference with a particular contagion model with stochastic intensities that is proposed by Bao et al. 2010. Stochastic interest rate is incorporated as well to account for positive correlation between spread and interest. Survival measure approach is adopted to calculate MtM of risk-free CDS and conditional survival probability of counterparty in defaultable environment. Semi-analytical solution for CVA is attained. Affine specification of intensities and interest rate concludes analytical expression for pre-default value of MtM. Numerical experiments at the last of this paper analyze the impact of contagion, volatility and correlation on CVA.

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    Bibliographic Info

    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 26277.

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    Date of creation: 28 Oct 2010
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    Handle: RePEc:pra:mprapa:26277

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    Keywords: Credit Value Adjustment; Contagion Model; Stochastic Intensities and Interest; Survival Measure; Affine Specification;

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    References

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    1. Bao, Qunfang & Li, Shenghong & Liu, Guimei, 2010. "Survival Measures and Interacting Intensity Model: with Applications in Guaranteed Debt Pricing," MPRA Paper 27698, University Library of Munich, Germany, revised 27 Dec 2010.
    2. P. Collin-Dufresne & R. Goldstein & J. Hugonnier, 2004. "A General Formula for Valuing Defaultable Securities," Econometrica, Econometric Society, Econometric Society, vol. 72(5), pages 1377-1407, 09.
    3. Philipp J. Schönbucher, 2000. "A Libor Market Model with Default Risk," Bonn Econ Discussion Papers, University of Bonn, Germany bgse15_2001, University of Bonn, Germany.
    4. Kwai Leung & Yue Kwok, 2009. "Counterparty Risk for Credit Default Swaps: Markov Chain Interacting Intensities Model with Stochastic Intensity," Asia-Pacific Financial Markets, Springer, vol. 16(3), pages 169-181, September.
    5. Damiano Brigo & Kyriakos Chourdakis, 2009. "Counterparty Risk For Credit Default Swaps: Impact Of Spread Volatility And Default Correlation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(07), pages 1007-1026.
    6. Christophette Blanchet-Scalliet & Fr\'ed\'eric Patras, 2008. "Counterparty risk valuation for CDS," Papers 0807.0309, arXiv.org.
    7. Robert A. Jarrow, 2001. "Counterparty Risk and the Pricing of Defaultable Securities," Journal of Finance, American Finance Association, American Finance Association, vol. 56(5), pages 1765-1799, October.
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