IDEAS home Printed from https://ideas.repec.org/p/rdg/icmadp/icma-dp2004-14.html
   My bibliography  Save this paper

Pricing Convertible Bonds by Simulation

Author

Listed:
  • Ali Bora Yigitsbasioglu

    (ICMA Centre, University of Reading)

  • Dmitri Lvov

    (ICMA Centre, University of Reading)

  • Naoufel El-Bachir

    (ICMA Centre, University of Reading)

Abstract

Convertible bonds are complex hybrid securities subject to multiple sources of risk. Many exhibit exotic path dependent features. Monte Carlo simulation methods are usually the favorite choice for solving high-dimensional problems and pricing path dependent securities. This paper breaks away from the tradition established in the literature of pricing convertible bonds with finite difference and lattice methods, and suggests a simulation methodology for convertible bond pricing. We introduce the dividend process for convertible bonds, and formulate the pricing problem according to the probabilistic martingale approach. The proposed methodology deals with callable and puttable convertible bonds. The early exercise rules are estimated by means of least squares regressions as in Longstaff and Schwartz (2001). The accuracy of the simulation algorithm is tested in the context of a two factor model. The algorithm performs fairly well, and shows potential for further extension to include many complexities inherent in convertible bonds, as well as additional risk factors.

Suggested Citation

  • 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, University of Reading, revised Aug 2004.
    • Handle: RePEc:rdg:icmadp:icma-dp2004-14
    as

    Download full text from publisher

    File URL: http://www.icmacentre.ac.uk/pdf/discussion/DP2004-15.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ali Bora Yigitbasioglu, 2001. "Pricing Convertible Bonds with Interest Rate, Equity, Credit and FX Risk," ICMA Centre Discussion Papers in Finance icma-dp2001-14, Henley Business School, University of Reading.
    2. 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..
    3. Brennan, Michael J. & Schwartz, Eduardo S., 1980. "Analyzing Convertible Bonds," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(4), pages 907-929, November.
    4. 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.
    5. 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.
    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. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    8. Jun-Koo, Kang & Lee, Yul W., 1996. "The pricing of convertible debt offerings," Journal of Financial Economics, Elsevier, vol. 41(2), pages 231-248, June.
    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. Christopher Beveridge & Mark Joshi, 2011. "Monte Carlo Bounds for Game Options Including Convertible Bonds," Management Science, INFORMS, vol. 57(5), pages 960-974, May.
    2. Yang, Jingyang & Choi, Yoon & Li, Shenghong & Yu, Jinping, 2010. "A note on "Monte Carlo analysis of convertible bonds with reset clause"," European Journal of Operational Research, Elsevier, vol. 200(3), pages 924-925, February.
    3. Fan, Chenxi & Luo, Xingguo & Wu, Qingbiao, 2017. "Stochastic volatility vs. jump diffusions: Evidence from the Chinese convertible bond market," International Review of Economics & Finance, Elsevier, vol. 49(C), pages 1-16.
    4. Jonathan A. Batten & Karren Lee-Hwei Khaw & Martin R. Young, 2014. "Convertible Bond Pricing Models," Journal of Economic Surveys, Wiley Blackwell, vol. 28(5), pages 775-803, December.
    5. Feng, Yun & Huang, Bing-hua & Young, Martin & Zhou, Qi-yuan, 2015. "Decomposing and valuing convertible bonds: A new method based on exotic options," Economic Modelling, Elsevier, vol. 47(C), pages 193-206.
    6. Tian‐Shyr Dai & Chen‐Chiang Fan & Liang‐Chih Liu & Chuan‐Ju Wang & Jr‐Yan Wang, 2022. "A stochastic‐volatility equity‐price tree for pricing convertible bonds with endogenous firm values and default risks determined by the first‐passage default model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(12), pages 2103-2134, December.
    7. Zhou, Qi-Yuan & Wu, Chong-Feng & Feng, Yun, 2007. "Decomposing and valuing callable convertible bonds: a new method based on exotic options," MPRA Paper 7421, University Library of Munich, Germany.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jonathan A. Batten & Karren Lee-Hwei Khaw & Martin R. Young, 2014. "Convertible Bond Pricing Models," Journal of Economic Surveys, Wiley Blackwell, vol. 28(5), pages 775-803, December.
    2. Tian‐Shyr Dai & Chen‐Chiang Fan & Liang‐Chih Liu & Chuan‐Ju Wang & Jr‐Yan Wang, 2022. "A stochastic‐volatility equity‐price tree for pricing convertible bonds with endogenous firm values and default risks determined by the first‐passage default model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(12), pages 2103-2134, December.
    3. Yuriy Zabolotnyuk & Robert Jones & Chris Veld, 2010. "An Empirical Comparison of Convertible Bond Valuation Models," Financial Management, Financial Management Association International, vol. 39(2), pages 675-706, June.
    4. 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.
    5. Augusto Castillo, 2004. "Firm and Corporate Bond Valuation: A Simulation Dynamic Programming Approach," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 41(124), pages 345-360.
    6. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    7. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    8. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    9. Yoram Landskroner & Alon Raviv, 2008. "The valuation of inflation‐indexed and FX convertible bonds," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 28(7), pages 634-655, July.
    10. Alex W.H. Chan & Nai-fu Chen, 2006. "Convertible Bond Underpricing: Renegotiable Covenants, Seasoning and Convergence," CIRJE F-Series CIRJE-F-437, CIRJE, Faculty of Economics, University of Tokyo.
    11. Fernández, Pablo, 1996. "Convertible bonds in Spain: A different security," IESE Research Papers D/311, IESE Business School.
    12. Alex W.H. Chan & Nai-fu Chen, 2006. "Convertible Bond Underpricing: Renegotiable Covenants, Seasoning and Convergence (Published in "Management Science", Vol. 53, No. 11, November 2007, pp. 1793.1814. )," CARF F-Series CARF-F-075, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    13. Finnerty, John D., 2015. "Valuing convertible bonds and the option to exchange bonds for stock," Journal of Corporate Finance, Elsevier, vol. 31(C), pages 91-115.
    14. Viral V. Acharya & Jennifer N. Carpenter, 2002. "Corporate Bond Valuation and Hedging with Stochastic Interest Rates and Endogenous Bankruptcy," The Review of Financial Studies, Society for Financial Studies, vol. 15(5), pages 1355-1383.
    15. Francesca Erica Di Girolamo & Francesca Campolongo & Jan De Spiegeleer & Wim Schoutens, 2017. "Contingent conversion convertible bond: New avenue to raise bank capital," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-31, March.
    16. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2011.
    17. Yang, Xiaofeng & Yu, Jinping & Xu, Mengna & Fan, Wenjing, 2018. "Convertible bond pricing with partial integro-differential equation model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 152(C), pages 35-50.
    18. Zhou, Qi-Yuan & Wu, Chong-Feng & Feng, Yun, 2007. "Decomposing and valuing callable convertible bonds: a new method based on exotic options," MPRA Paper 7421, University Library of Munich, Germany.
    19. 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.
    20. Esteghamat, Kian, 2003. "A boundary crossing model of counterparty risk," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1771-1799, August.

    More about this item

    Statistics

    Access and download statistics

    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:rdg:icmadp:icma-dp2004-14. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Marie Pearson (email available below). General contact details of provider: https://edirc.repec.org/data/bsrdguk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.