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A lattice approach for pricing convertible bond asset swaps with market risk and counterparty risk

  • Xu, Ruxing
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    This paper proposes a new lattice framework for valuing convertible bonds (CBs) and asset swaps on CBs (CBASs) with market risk and counterparty risk, where interest rate is assumed to follow a mean-reverting square root process. The reduced-form approach is generalized to include a constant elasticity of variance (CEV) process for equity price prior to default. In order to approximate the CEV process while taking into account stochastic interest rate and the correlation between stock price and interest rate, I first propose a transform that is uncorrelated with interest rate, and then construct a new lattice method which can ensure the validity of branching probabilities for all nodes. The lattice framework performs properly when it is used to value European call options. Based on the empirical results in Duffie et al. (J. Fin. Econ. 83(3): 635-665, 2007) and Jankowitsch et al. (J. Bank. Fin. 32(7): 1269-1285, 2008), a novel default intensity process is constructed which is specified as a function of time, stock price, and interest rate. When valuing the asset swaps, the counterparty risk is taken into consideration. Based on the results of the numerical experiments, the impacts of different parameters on the prices of CBs and CBASs are explained.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0264999311001271
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    Article provided by Elsevier in its journal Economic Modelling.

    Volume (Year): 28 (2011)
    Issue (Month): 5 (September)
    Pages: 2143-2153

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    Handle: RePEc:eee:ecmode:v:28:y:2011:i:5:p:2143-2153
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/30411

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    1. Brennan, M J & Schwartz, Eduardo S, 1977. "Convertible Bonds: Valuation and Optimal Strategies for Call and Conversion," Journal of Finance, American Finance Association, vol. 32(5), pages 1699-1715, December.
    2. Vadim Linetsky, 2006. "Pricing Equity Derivatives Subject To Bankruptcy," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 255-282.
    3. Darrell Duffie & Leandro Siata & Ke Wang, 2006. "Multi-Period Corporate Default Prediction With Stochastic Covariates," NBER Working Papers 11962, National Bureau of Economic Research, Inc.
    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. 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.
    6. Akihiko Takahashi & Takao Kobayashi & Naruhisa Nakagawa, 2001. "Pricing Convertible Bonds with Default Risk: A Duffie-Singleton Approach," CIRJE F-Series CIRJE-F-140, CIRJE, Faculty of Economics, University of Tokyo.
    7. 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.
    8. Nelson, Daniel B & Ramaswamy, Krishna, 1990. "Simple Binomial Processes as Diffusion Approximations in Financial Models," Review of Financial Studies, Society for Financial Studies, vol. 3(3), pages 393-430.
    9. Xin Guo & Robert A. Jarrow & Yan Zeng, 2009. "Modeling The Recovery Rate In A Reduced Form Model," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 73-97.
    10. Jankowitsch, Rainer & Pullirsch, Rainer & Veza, Tanja, 2008. "The delivery option in credit default swaps," Journal of Banking & Finance, Elsevier, vol. 32(7), pages 1269-1285, July.
    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. 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.
    13. K. G. Nyborg, 1996. "The use and pricing of convertible bonds," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(3), pages 167-190.
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