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

Listed author(s):
  • Xiao, Tim
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    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.

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    File URL: https://mpra.ub.uni-muenchen.de/47366/1/MPRA_paper_47366.pdf
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    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 47366.

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    Date of creation: 21 May 2013
    Handle: RePEc:pra:mprapa:47366
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    1. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Duffie, Darrell & Huang, Ming, 1996. " Swap Rates and Credit Quality," Journal of Finance, American Finance Association, vol. 51(3), pages 921-949, July.
    8. 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, 06.
    9. 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.
    10. 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.
    11. 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.
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