IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v366y2006icp449-462.html
   My bibliography  Save this article

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

Author

Listed:
  • Gong, Pu
  • He, Zhiwei
  • Zhu, Song-Ping

Abstract

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.

Suggested Citation

  • Gong, Pu & He, Zhiwei & Zhu, Song-Ping, 2006. "Pricing convertible bonds based on a multi-stage compound-option model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 449-462.
  • Handle: RePEc:eee:phsmap:v:366:y:2006:i:c:p:449-462
    DOI: 10.1016/j.physa.2006.02.035
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843710600197X
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    2. Geske, Robert, 1979. "The valuation of compound options," Journal of Financial Economics, Elsevier, vol. 7(1), pages 63-81, March.
    3. Roll, Richard, 1977. "An analytic valuation formula for unprotected American call options on stocks with known dividends," Journal of Financial Economics, Elsevier, vol. 5(2), pages 251-258, November.
    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..
    5. 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.
    6. Geske, Robert & Johnson, Herb E, 1984. " The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-1524, December.
    7. Geske, Robert, 1977. "The Valuation of Corporate Liabilities as Compound Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 541-552, November.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gong, Pu & Dai, Jun, 2017. "Pricing real estate index options under stochastic interest rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 309-323.
    2. Egami, Masahiko, 2010. "A game options approach to the investment problem with convertible debt financing," Journal of Economic Dynamics and Control, Elsevier, vol. 34(8), pages 1456-1470, August.
    3. Liang, Zhaohui & Wang, Wei & Li, Shusheng, 2012. "Decomposition valuation of complex real options embedded in creative financial leases," Economic Modelling, Elsevier, vol. 29(6), pages 2627-2631.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:366:y:2006:i:c:p:449-462. 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: (Dana Niculescu). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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 CitEc recognized a reference but did not link an item in RePEc 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 RePEc Author Service 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.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.