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Pricing convertible bonds based on a multi-stage compound-option model

Listed author(s):
  • Gong, Pu
  • He, Zhiwei
  • Zhu, Song-Ping
Registered author(s):

    In this paper, we introduce the concept of multi-stage compound options to the valuation of convertible bonds (CBs). Rather than evaluating a nested high-dimensional integral that has arisen from the valuation of multi-stage compound options, we found that adopting the finite difference method (FDM) to solve the Black–Scholes equation for each stage actually resulted in a better numerical efficiency. By comparing our results with those obtained by solving the Black–Scholes equation directly, we can show that the new approach does provide an approximation approach for the valuation of CBs and demonstrate that it offers a great potential for a further extension to CBs with more complex structures such as those with call and/or put provisions.

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    File URL: http://www.sciencedirect.com/science/article/pii/S037843710600197X
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    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 366 (2006)
    Issue (Month): C ()
    Pages: 449-462

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    Handle: RePEc:eee:phsmap:v:366:y:2006:i:c:p:449-462
    DOI: 10.1016/j.physa.2006.02.035
    Contact details of provider: Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

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    1. Breen, Richard, 1991. "The Accelerated Binomial Option Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(02), pages 153-164, June.
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    4. Robert A. Jarrow & Stuart M. Turnbull, 2008. "Pricing Derivatives on Financial Securities Subject to Credit Risk," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 17, pages 377-409 World Scientific Publishing Co. Pte. Ltd..
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    8. Shastri, Kuldeep & Tandon, Kishore, 1987. "Valuation of American options on foreign currency," Journal of Banking & Finance, Elsevier, vol. 11(2), pages 245-269, June.
    9. Bunch, David S & Johnson, Herb, 1992. " A Simple and Numerically Efficient Valuation Method for American Puts Using a Modified Geske-Johnson Approach," Journal of Finance, American Finance Association, vol. 47(2), pages 809-816, June.
    10. Ingersoll, Jonathan E, Jr, 1977. "An Examination of Corporate Call Policies on Convertible Securities," Journal of Finance, American Finance Association, vol. 32(2), pages 463-478, May.
    11. McConnell, John J & Schwartz, Eduardo S, 1986. " LYON Taming," Journal of Finance, American Finance Association, vol. 41(3), pages 561-576, July.
    12. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    13. Shastri, Kuldeep & Tandon, Kishore, 1986. "An Empirical Test of a Valuation Model for American Options on Futures Contracts," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(04), pages 377-392, December.
    14. Bertram, William K, 2004. "An empirical investigation of Australian Stock Exchange data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 341(C), pages 533-546.
    15. Trigeorgis, Lenos, 1991. "A Log-Transformed Binomial Numerical Analysis Method for Valuing Complex Multi-Option Investments," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(03), pages 309-326, September.
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