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Finite-time survival probability and credit default swaps pricing under geometric Lévy markets

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  • Hao, Xuemiao
  • Li, Xuan
  • Shimizu, Yasutaka

Abstract

We study the first-passage time over a fixed threshold for a pure-jump subordinator with negative drift. We obtain a closed-form formula for its survival function in terms of marginal density functions of the subordinator. We then use this formula to calculate finite-time survival probabilities in a structural model for credit risk, and thus obtain a closed-form pricing formula for a single-name credit default swap (CDS). This pricing formula is well calibrated on market CDS quotes. In particular, it explains why the par CDS credit spread is not negligible when the maturity becomes short.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:53:y:2013:i:1:p:14-23
    DOI: 10.1016/j.insmatheco.2013.04.003
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    Cited by:

    1. Davide Radi & Vu Phuong Hoang & Gabriele Torri & Hana Dvořáčková, 2021. "A revised version of the Cathcart & El-Jahel model and its application to CDS market," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 669-705, December.
    2. Ballestra, Luca Vincenzo & Pacelli, Graziella & Radi, Davide, 2020. "Modeling CDS spreads: A comparison of some hybrid approaches," Journal of Empirical Finance, Elsevier, vol. 57(C), pages 107-124.
    3. Shimizu, Yasutaka & Zhang, Zhimin, 2017. "Estimating Gerber–Shiu functions from discretely observed Lévy driven surplus," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 84-98.
    4. 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.
    5. 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; Finite-time survival probability; First-passage time; Lévy process; 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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