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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- 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 449-470, May.
- 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 & 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.
- 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.
- 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.
- 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.
- 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.
- K. G. Nyborg, 1996. "The use and pricing of convertible bonds," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(3), pages 167-190.
- 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.
- Vadim Linetsky, 2006. "Pricing Equity Derivatives Subject To Bankruptcy," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 255-282.
- 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.
- 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.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:eee:ecmode:v:28:y:2011:i:5:p:2143-2153. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.