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A reflection principle for correlated defaults

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  • Patras, Frédéric

Abstract

The correct valuation of the so-called "correlation products" in the credit risk market such as n-th-to-default swaps or CDOs requires a better understanding of higher dimensional barrier default phenomena. We introduce a reflection principle suited for the pricing of credit derivatives on two securities, paving the way for the development of new methods in the field. For that purpose, we introduce new processes, the distributions of which involve generalized Bessel functions. As an application, we derive a closed formula for second-to-default digital swaps, under the standard Black-Cox hypothesis on the conditions triggering default.

Suggested Citation

  • Patras, Frédéric, 2006. "A reflection principle for correlated defaults," Stochastic Processes and their Applications, Elsevier, vol. 116(4), pages 690-698, April.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:4:p:690-698
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    References listed on IDEAS

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    1. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-367, May.
    2. Hua He & William P. Keirstead & Joachim Rebholz, 1998. "Double Lookbacks," Mathematical Finance, Wiley Blackwell, vol. 8(3), pages 201-228, July.
    3. Zhou, Chunsheng, 2001. "An Analysis of Default Correlations and Multiple Defaults," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 555-576.
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