A lattice approach for pricing convertible bond asset swaps with market risk and counterparty risk
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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- 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.
- Duffie, Darrell & Saita, Leandro & Wang, Ke, 2007. "Multi-period corporate default prediction with stochastic covariates," Journal of Financial Economics, Elsevier, vol. 83(3), pages 635-665, March.
- Darrel Duffie & Leandro Saita & Ke Wang, 2005. "Multi-Period Corporate Default Prediction With Stochastic Covariates," CIRJE F-Series CIRJE-F-373, CIRJE, Faculty of Economics, University of Tokyo.
- Darrel Duffie & Leandro Saita & Ke Wang, 2005. "Multi-Period Corporate Default Prediction With Stochastic Covariates," CARF F-Series CARF-F-047, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
- Manuel Ammann & Axel Kind & Christian Wilde, 2005.
"Simulation-Based Pricing of Convertible Bonds,"
- Merton, Robert C., 1973.
"On the pricing of corporate debt: the risk structure of interest rates,"
684-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- 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.
- 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.
- 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.
- 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.
- 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.
- K. G. Nyborg, 1996. "The use and pricing of convertible bonds," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(3), pages 167-190.
- 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.
- 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.
- 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.
- 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.
- Vadim Linetsky, 2006. "Pricing Equity Derivatives Subject To Bankruptcy," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 255-282.
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