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

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  • Olivier Le Courtois
  • François Quittard-Pinon

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

Suggested Citation

  • Olivier Le Courtois & François Quittard-Pinon, 2006. "Risk-neutral and actual default probabilities with an endogenous bankruptcy jump-diffusion model," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 13(1), pages 11-39, March.
  • Handle: RePEc:kap:apfinm:v:13:y:2006:i:1:p:11-39
    DOI: 10.1007/s10690-007-9033-1
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    References listed on IDEAS

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    1. Francis A. Longstaff & Sanjay Mithal & Eric Neis, 2005. "Corporate Yield Spreads: Default Risk or Liquidity? New Evidence from the Credit Default Swap Market," Journal of Finance, American Finance Association, vol. 60(5), pages 2213-2253, October.
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    4. Robert A. Jarrow & David Lando & Stuart M. Turnbull, 2008. "A Markov Model for the Term Structure of Credit Risk Spreads," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 18, pages 411-453, World Scientific Publishing Co. Pte. Ltd..
    5. 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.
    6. Edward I. Altman, 1968. "The Prediction Of Corporate Bankruptcy: A Discriminant Analysis," Journal of Finance, American Finance Association, vol. 23(1), pages 193-194, March.
    7. 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.
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    11. 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.
    12. Thi Thanh Binh Dao, 2005. "Double Exponential Jump : A Structural Model," Post-Print halshs-00164806, HAL.
    13. 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.
    14. Edward I. Altman, 1968. "Financial Ratios, Discriminant Analysis And The Prediction Of Corporate Bankruptcy," Journal of Finance, American Finance Association, vol. 23(4), pages 589-609, September.
    15. 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.
    16. Usabel, Miguel, 1999. "Calculating multivariate ruin probabilities via Gaver-Stehfest inversion technique," Insurance: Mathematics and Economics, Elsevier, vol. 25(2), pages 133-142, November.
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    Cited by:

    1. Walter, Christian, 2016. "The financial Logos: The framing of financial decision-making by mathematical modelling," Research in International Business and Finance, Elsevier, vol. 37(C), pages 597-604.
    2. 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.
    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.
    4. 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;Associazione per la Matematica, vol. 31(1), pages 51-72, May.
    5. Hainaut, Donatien, 2015. "Evaluation and default time for companies with uncertain cash flows," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 276-285.

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    More about this item

    Keywords

    Cumulative default probability; Structural model; Jump-diffusion; Endogenous capital structure; Esscher transform; Kou processes; G32; G33;
    All these keywords.

    JEL classification:

    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • G33 - Financial Economics - - Corporate Finance and Governance - - - Bankruptcy; Liquidation

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