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Decomposing and valuing callable convertible bonds: a new method based on exotic options

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  • Zhou, Qi-Yuan
  • Wu, Chong-Feng
  • Feng, Yun
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    Abstract

    In the framework of Black-Scholes-Merton option pricing models, by employing exotic options instead of plain options or warrants, this paper presents an equivalent decomposition method for usual Callable Convertible Bonds (CCB). Furthermore, the analytic valuation formulae for CCB are worked out by using the analytic formulae for those simpler securities decomposed from CCB. Moreover, this method is validated by comparing with Monte Carlo simulation. Besides, the effects of call clauses, coupon clauses and soft call condition clauses are analyzed respectively. These give lots of new insights into the valuation and analysis of CCB and much help to hedge their risks.

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    File URL: http://mpra.ub.uni-muenchen.de/7421/
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    Bibliographic Info

    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 7421.

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    Date of creation: 16 Feb 2007
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    Handle: RePEc:pra:mprapa:7421

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    Keywords: Callable convertible bonds; Equivalent decomposition; Up-and-out calls; American binary calls; Derivative pricing;

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    1. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    2. 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.
    3. Ali Bora Yigibasioglu & Carol Alexandra, 2004. "An Uncertain Volatility Explanation for Delayed Calls of Convertible Bonds," ICMA Centre Discussion Papers in Finance icma-dp2004-07, Henley Business School, Reading University.
    4. 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.
    5. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    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. K. G. Nyborg, 1996. "The use and pricing of convertible bonds," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(3), pages 167-190.
    8. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
    9. Ingersoll, Jonathan Jr., 1977. "A contingent-claims valuation of convertible securities," Journal of Financial Economics, Elsevier, vol. 4(3), pages 289-321, May.
    10. Ali Bora Yigitsbasioglu & Dmitri Lvov & Naoufel El-Bachir, 2004. "Pricing Convertible Bonds by Simulation," ICMA Centre Discussion Papers in Finance icma-dp2004-14, Henley Business School, Reading University, revised Aug 2004.
    11. McConnell, John J & Schwartz, Eduardo S, 1986. " LYON Taming," Journal of Finance, American Finance Association, vol. 41(3), pages 561-76, July.
    12. Barone-Adesi, Giovanni & Bermudez, Ana & Hatgioannides, John, 2003. "Two-factor convertible bonds valuation using the method of characteristics/finite elements," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1801-1831, August.
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