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A simple iteration algorithm to price perpetual Bermudan options under the lognormal jump‐diffusion‐ruin process

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  • San‐Lin Chung
  • Jr‐Yan Wang

Abstract

We propose an analytical‐form framework for pricing perpetual Bermudan options (PBOs) under the lognormal jump‐diffusion‐ruin model of Merton (1976). We first analytically derive the holding and early exercise values of PBOs. The optimal exercise boundary of the PBO, determined by equating the holding and early exercise values, is then solved using an iteration algorithm. We finally evaluate the PBO by taking the expectation of the option prices at the subsequent exercisable date and discounting it at the risk‐free rate. The numerical results indicate that our method is far more efficient than the competing methods in the literature for pricing PBOs.

Suggested Citation

  • San‐Lin Chung & Jr‐Yan Wang, 2018. "A simple iteration algorithm to price perpetual Bermudan options under the lognormal jump‐diffusion‐ruin process," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(8), pages 898-924, August.
    • Handle: RePEc:wly:jfutmk:v:38:y:2018:i:8:p:898-924
    DOI: 10.1002/fut.21911
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    1. Bart M. Lambrecht & Stewart C. Myers, 2007. "A Theory of Takeovers and Disinvestment," Journal of Finance, American Finance Association, vol. 62(2), pages 809-845, April.
    2. Muthuraman, Kumar, 2008. "A moving boundary approach to American option pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3520-3537, November.
    3. Leland, Hayne E, 1994. "Corporate Debt Value, Bond Covenants, and Optimal Capital Structure," Journal of Finance, American Finance Association, vol. 49(4), pages 1213-1252, September.
    4. S. I. Boyarchenko & S. Z. Levendorskii, 2002. "Pricing of perpetual Bermudan options," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 432-442.
    5. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    6. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(4), pages 707-727.
    7. Amin, Kaushik I, 1993. "Jump Diffusion Option Valuation in Discrete Time," Journal of Finance, American Finance Association, vol. 48(5), pages 1833-1863, December.
    8. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    9. Suresh Sundaresan & Neng Wang, 2007. "Investment under Uncertainty with Strategic Debt Service," American Economic Review, American Economic Association, vol. 97(2), pages 256-261, May.
    10. 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.
    11. Andricopoulos, Ari D. & Widdicks, Martin & Duck, Peter W. & Newton, David P., 2003. "Universal option valuation using quadrature methods," Journal of Financial Economics, Elsevier, vol. 67(3), pages 447-471, March.
    12. Geske, Robert & Shastri, Kuldeep, 1985. "Valuation by Approximation: A Comparison of Alternative Option Valuation Techniques," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 20(1), pages 45-71, March.
    13. Quigg, Laura, 1993. "Empirical Testing of Real Option-Pricing Models," Journal of Finance, American Finance Association, vol. 48(2), pages 621-640, June.
    14. Ju, Nengjiu, 1998. "Pricing an American Option by Approximating Its Early Exercise Boundary as a Multipiece Exponential Function," The Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 627-646.
    15. Guthrie, Graeme, 2007. "Missed Opportunities: Optimal Investment Timing When Information is Costly," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(2), pages 467-488, June.
    16. Jingtang Ma & Peng Luo, 2012. "Integral Equation Methods for Pricing Perpetual Bermudan Options," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 2(3), pages 1-3.
    17. Glenn W. Boyle & Graeme A. Guthrie, 2003. "Investment, Uncertainty, and Liquidity," Journal of Finance, American Finance Association, vol. 58(5), pages 2143-2166, October.
    18. Yoshifumi Muroi & Takashi Yamada, 2008. "An Explicit Finite Difference Approach to the Pricing Problems of Perpetual Bermudan Options," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 15(3), pages 229-253, December.
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