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Is the Jump-Diffusion Model a Good Solution for Credit Risk Modeling? The Case of Convertible Bonds

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  • Xiao, Tim

Abstract

Tim Xiao: This paper argues that the reduced-form jump diffusion model may not be appropriate for credit risk modeling. To correctly value hybrid defaultable financial instruments, e.g., convertible bonds, we present a new framework that relies on the probability distribution of a default jump rather than the default jump itself, as the default jump is usually inaccessible. The model is quite accurate. A prevailing belief in the market is that convertible arbitrage is mainly due to convertible underpricing. Empirically, however, we do not find evidence supporting the underpricing hypothesis. Instead, we find that convertibles have relatively large position gammas. As a typical convertible arbitrage strategy employs delta-neutral hedging, a large positive gamma can make the portfolio high profitable, especially for a large movement in the underlying stock price.

Suggested Citation

  • Xiao, Tim, 2013. "Is the Jump-Diffusion Model a Good Solution for Credit Risk Modeling? The Case of Convertible Bonds," MPRA Paper 47366, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:47366
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    File URL: https://mpra.ub.uni-muenchen.de/47366/1/MPRA_paper_47366.pdf
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    References listed on IDEAS

    as
    1. Peter Carr & Vadim Linetsky, 2006. "A jump to default extended CEV model: an application of Bessel processes," Finance and Stochastics, Springer, vol. 10(3), pages 303-330, September.
    2. Yuriy Zabolotnyuk & Robert Jones & Chris Veld, 2010. "An Empirical Comparison of Convertible Bond Valuation Models," Financial Management, Financial Management Association International, vol. 39(2), pages 675-706, June.
    3. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    4. Ammann, Manuel & Kind, Axel & Wilde, Christian, 2008. "Simulation-based pricing of convertible bonds," Journal of Empirical Finance, Elsevier, vol. 15(2), pages 310-331, March.
    5. 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.
    6. Ederington, Louis H & Lee, Jae Ha, 1993. " How Markets Process Information: News Releases and Volatility," Journal of Finance, American Finance Association, vol. 48(4), pages 1161-1191, September.
    7. Choi, Darwin & Getmansky, Mila & Tookes, Heather, 2009. "Convertible bond arbitrage, liquidity externalities, and stock prices," Journal of Financial Economics, Elsevier, vol. 91(2), pages 227-251, February.
    8. Brennan, Michael J. & Schwartz, Eduardo S., 1980. "Analyzing Convertible Bonds," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(04), pages 907-929, November.
    9. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    10. Duffie, Darrell & Huang, Ming, 1996. " Swap Rates and Credit Quality," Journal of Finance, American Finance Association, vol. 51(3), pages 921-949, July.
    11. Ammann, Manuel & Kind, Axel & Wilde, Christian, 2003. "Are convertible bonds underpriced? An analysis of the French market," Journal of Banking & Finance, Elsevier, vol. 27(4), pages 635-653, April.
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    More about this item

    Keywords

    jump diffusion model; hybrid financial instrument; convertible bond; convertible underpricing; convertible arbitrage; default time approach; default probability (intensity) approach; asset pricing; credit risk modeling.;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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