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Pricing credit default swaps with a random recovery rate by a double inverse Fourier transform

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  • Hao, Xuemiao
  • Li, Xuan

Abstract

We evaluate the par spread for a single-name credit default swap with a random recovery rate. It is carried out under the framework of a structural default model in which the asset-value process is of infinite activity but finite variation. The recovery rate is assumed to depend on the undershoot of the asset value below the default threshold when default occurs. The key part is to evaluate a generalized expected discounted penalty function, which is a special case of the so-called Gerber–Shiu function in actuarial ruin theory. We first obtain its double Laplace transform in time and in spatial variable, and then implement a numerical Fourier inversion integration. Numerical experiments show that our algorithm gives accurate results within reasonable time and different shapes of spread curve can be obtained.

Suggested Citation

  • Hao, Xuemiao & Li, Xuan, 2015. "Pricing credit default swaps with a random recovery rate by a double inverse Fourier transform," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 103-110.
    • Handle: RePEc:eee:insuma:v:65:y:2015:i:c:p:103-110
    DOI: 10.1016/j.insmatheco.2015.09.005
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    References listed on IDEAS

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    5. Hao, Xuemiao & Li, Xuan & Shimizu, Yasutaka, 2013. "Finite-time survival probability and credit default swaps pricing under geometric Lévy markets," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 14-23.
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    Cited by:

    1. Shi, Xiaojun & Tang, Qihe & Yuan, Zhongyi, 2017. "A limit distribution of credit portfolio losses with low default probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 156-167.
    2. Cantia, Catalin & Tunaru, Radu, 2017. "A factor model for joint default probabilities. Pricing of CDS, index swaps and index tranches," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 21-35.

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    More about this item

    Keywords

    Credit default swap; Infinite activity; Lévy process; Random recovery rate; Structural model;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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