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Risk-neutral and actual default probabilities with an endogenous bankruptcy jump-diffusion model

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  • Olivier Le Courtois

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  • François Quittard-Pinon

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    Abstract

    This paper focuses on historical and risk-neutral default probabilities in a structural model, when the firm assets dynamics are modeled by a double exponential jump diffusion process. Relying on the Leland [(1994a) Journal of Finance, 49, 1213–1252; (1994b) Bond prices, yield spreads, and optimal capital structure with default risk. Working paper no. 240, IBER, University of California, Berkeley] or Leland and Toft [(1996) Journal of Finance, 51(3), 987–1019] endogenous structural approaches, as formalized by Hilberink and Rogers [(2002) Finance and Stochastics, 6(2), 237–263], this article gives a coherent construction of historical default probabilities. The risk-neutral world where evolve the firm assets, modeled by a class of geometric Lévy processes, is constructed based on the Esscher measure, yielding useful and new analytical relations between historical and risk-neutral probabilities. We do a complete numerical analysis of the predictions of our framework, and compare these predictions with actual data. In particular, this new framework displays an enhanced predictive power w.r.t. current Gaussian endogenous structural models. Copyright Springer Science+Business Media, LLC 2006

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    File URL: http://hdl.handle.net/10.1007/s10690-007-9033-1
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    Bibliographic Info

    Article provided by Springer in its journal Asia-Pacific Financial Markets.

    Volume (Year): 13 (2006)
    Issue (Month): 1 (March)
    Pages: 11-39

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    Handle: RePEc:kap:apfinm:v:13:y:2006:i:1:p:11-39

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    Web page: http://springerlink.metapress.com/link.asp?id=102851

    Related research

    Keywords: Cumulative default probability; Structural model; Jump-diffusion; Endogenous capital structure; Esscher transform; Kou processes; G32; G33;

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    References

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    1. Leland, Hayne E & Toft, Klaus Bjerre, 1996. " Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads," Journal of Finance, American Finance Association, vol. 51(3), pages 987-1019, July.
    2. 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 351-67, May.
    3. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-70, May.
    4. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    5. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    6. Usabel, Miguel, 1999. "Calculating multivariate ruin probabilities via Gaver-Stehfest inversion technique," Insurance: Mathematics and Economics, Elsevier, vol. 25(2), pages 133-142, November.
    7. Bianca Hilberink & L.C.G. Rogers, 2002. "Optimal capital structure and endogenous default," Finance and Stochastics, Springer, vol. 6(2), pages 237-263.
    8. Crouhy, Michel & Galai, Dan & Mark, Robert, 2000. "A comparative analysis of current credit risk models," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 59-117, January.
    9. Longstaff, Francis A & Schwartz, Eduardo S, 1995. " A Simple Approach to Valuing Risky Fixed and Floating Rate Debt," Journal of Finance, American Finance Association, vol. 50(3), pages 789-819, July.
    10. Jarrow, Robert A & Lando, David & Turnbull, Stuart M, 1997. "A Markov Model for the Term Structure of Credit Risk Spreads," Review of Financial Studies, Society for Financial Studies, vol. 10(2), pages 481-523.
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    Cited by:
    1. Chuancun Yin & Yuzhen Wen & Zhaojun Zong & Ying Shen, 2013. "The first passage time problem for mixed-exponential jump processes with applications in insurance and finance," Papers 1302.6762, arXiv.org, revised Jun 2014.
    2. Olivier Le Courtois & François Quittard-Pinon, 2008. "The optimal capital structure of the firm with stable Lévy assets returns," Decisions in Economics and Finance, Springer, vol. 31(1), pages 51-72, May.
    3. Hayette Gatfaoui, 2010. "Investigating the dependence structure between credit default swap spreads and the U.S. financial market," Annals of Finance, Springer, vol. 6(4), pages 511-535, October.

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