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Valuation of credit default swaps and swaptions

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  • Farshid Jamshidian

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    Abstract

    This paper presents a conceptual and general framework for valuation of single-name credit derivatives. The general subfiltration approach of [J-R] to modelling default risk, which includes the Cox-process setting of [L], is integrated with a numeraire invariant approach. Several known results are reformulated and extended in this framework. New concepts and results are presented for change of numeraire in presence of default and valuation of credit swaptions. A new formula on fractional recovery of pre-default value is derived, generalizing that of [D-S]. A Black-Scholes formula for credit default swaptions due to [S] is shown to serve as a least-squares approximation to the general case. Copyright Springer-Verlag Berlin/Heidelberg 2004

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    File URL: http://hdl.handle.net/10.1007/s00780-004-0122-y
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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 8 (2004)
    Issue (Month): 3 (08)
    Pages: 343-371

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    Handle: RePEc:spr:finsto:v:8:y:2004:i:3:p:343-371

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    Web page: http://www.springerlink.com/content/101164/

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    Related research

    Keywords: Credit default swap; swaption; swap rate; subfiltration; conditional survival probability; preprice; prenumeraire; recovery; coadapted numeraires;

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    Cited by:
    1. Damiano Brigo & Naoufel El-Bachir, 2006. "Credit Derivatives Pricing with a Smile-Extended Jump Stochastic Intensity Model," ICMA Centre Discussion Papers in Finance icma-dp2006-13, Henley Business School, Reading University.
    2. Tomasz Bielecki & Monique Jeanblanc & Marek Rutkowski, 2011. "Hedging of a credit default swaption in the CIR default intensity model," Finance and Stochastics, Springer, vol. 15(3), pages 541-572, September.
    3. Carl Chiarella & Viviana Fanelli & Silvana Musti, 2009. "Modelling the Evolution of Credit Spreads Using the Cox Process Within the HJM Framework A CDS Option Pricing Model," Research Paper Series 255, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Naoufel El-Bachir & Damiano Brigo, 2008. "An analytically tractable time-changed jump-diffusion default intensity model," ICMA Centre Discussion Papers in Finance icma-dp2008-06, Henley Business School, Reading University.
    5. Massimo Morini & Damiano Brigo, 2008. "Arbitrage-free Pricing of Credit Index Options: The no-armageddon pricing measure and the role of correlation after the subprime crisis," Papers 0812.4156, arXiv.org.
    6. Schrager, David F., 2006. "Affine stochastic mortality," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 81-97, February.
    7. Damiano Brigo & Naoufel El-Bachir, 2008. "An exact formula for default swaptions' pricing in the SSRJD stochastic intensity model," Papers 0812.4199, arXiv.org.
    8. Chen, Bingzheng & Zhang, Lihong & Zhao, Lin, 2010. "On the robustness of longevity risk pricing," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 358-373, December.

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