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Unilateral CVA for CDS in a contagion model with stochastic pre-intensity and interest

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  • Bao, Qunfang
  • Chen, Si
  • Li, Shenghong

Abstract

Price of a financial derivative with unilateral counterparty credit risk equals to the price of an otherwise risk-free derivative minus a credit value adjustment (CVA) component, which can be seen as a call option on investor's NPV with strike 0. Thus modeling volatility of NPV is the foundation for CVA valuation. This paper assumes that default times of counterparty and reference firm follow a special contagion model with stochastic pre-intensities that allows for explicit formulas for default probabilities. Stochastic interest rate is also incorporated to account for positive correlation between pre-intensity and interest. Survival measure approach is employed to calculate NPV of a risk-free CDS, and semi-analytical solution for CVA is obtained through affine specifications. Numerical analysis shows that contagion has more significant impact on CVA than diffusion of pre-intensities, and the positive correlation between interest and reference firm's pre-intensity has monotonic decreasing impact on CVA.

Suggested Citation

  • Bao, Qunfang & Chen, Si & Li, Shenghong, 2012. "Unilateral CVA for CDS in a contagion model with stochastic pre-intensity and interest," Economic Modelling, Elsevier, vol. 29(2), pages 471-477.
    • Handle: RePEc:eee:ecmode:v:29:y:2012:i:2:p:471-477
    DOI: 10.1016/j.econmod.2011.12.002
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    References listed on IDEAS

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    1. Fan Yu, 2007. "Correlated Defaults In Intensity‐Based Models," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 155-173, April.
    2. P. Collin-Dufresne & R. Goldstein & J. Hugonnier, 2004. "A General Formula for Valuing Defaultable Securities," Econometrica, Econometric Society, vol. 72(5), pages 1377-1407, September.
    3. Kwai Leung & Yue Kwok, 2009. "Counterparty Risk for Credit Default Swaps: Markov Chain Interacting Intensities Model with Stochastic Intensity," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 16(3), pages 169-181, September.
    4. Robert A. Jarrow & Fan Yu, 2008. "Counterparty Risk and the Pricing of Defaultable Securities," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 20, pages 481-515, World Scientific Publishing Co. Pte. Ltd..
    5. Christophette Blanchet-Scalliet & Fr'ed'eric Patras, 2008. "Counterparty risk valuation for CDS," Papers 0807.0309, arXiv.org.
    6. Brian Huge & David Lando, 1999. "Swap Pricing with Two-Sided Default Risk in a Rating-Based Model," Review of Finance, European Finance Association, vol. 3(3), pages 239-268.
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    Cited by:

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    2. Boros, Péter, 2020. "A hitelminősítői bejelentések fertőző hatásai és a hitelértékelési kiigazítás [Rating migration, credit risk contagion and Credit Valuation Adjustment]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(2), pages 140-163.
    3. Yinghui Dong & Guojing Wang & Kam C. Yuen, 2014. "Bilateral Counterparty Risk Valuation on a CDS with a Common Shock Model," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 643-673, September.
    4. Samaniego-Medina, Reyes & Trujillo-Ponce, Antonio & Parrado-Martínez, Purificación & di Pietro, Filippo, 2016. "Determinants of bank CDS spreads in Europe," Journal of Economics and Business, Elsevier, vol. 86(C), pages 1-15.
    5. Dong, Yinghui & Wang, Guojing, 2014. "Bilateral counterparty risk valuation for credit default swap in a contagion model using Markov chain," Economic Modelling, Elsevier, vol. 40(C), pages 91-100.

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    More about this item

    Keywords

    Credit value adjustment; Contagion model; Stochastic pre-intensities and interest; Survival measure; Affine specification;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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