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Valuing American options using multi-step rebate options

Author

Listed:
  • Lee, Hangsuck
  • Ha, Hongjun
  • Lee, Gaeun
  • Lee, Minha

Abstract

The determination of optimal exercise boundaries is a critical aspect of pricing American options, which often requires costly numerical methods. This paper proposes a new approach that employs multi-step rebate options to approximate American option prices. Since the rebate options offer payoffs when the multi-step boundaries are touched, the prices of American options are estimated by maximizing the multi-step rebate option prices, and the optimal multi-step barriers replace the true optimal exercise boundaries. To this end, the closed-form pricing formulas for multi-step rebate options are derived and utilized to approximate several American option prices. Through extensive numerical experiments, we demonstrate the validity and performance of our approach.

Suggested Citation

  • Lee, Hangsuck & Ha, Hongjun & Lee, Gaeun & Lee, Minha, 2024. "Valuing American options using multi-step rebate options," The North American Journal of Economics and Finance, Elsevier, vol. 74(C).
    • Handle: RePEc:eee:ecofin:v:74:y:2024:i:c:s1062940824001529
    DOI: 10.1016/j.najef.2024.102227
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    References listed on IDEAS

    as
    1. Lee, Hangsuck & Ha, Hongjun & Lee, Minha, 2021. "Valuation of piecewise linear barrier options," The North American Journal of Economics and Finance, Elsevier, vol. 58(C).
    2. Mark Broadie & Jérôme Detemple, 1997. "The Valuation of American Options on Multiple Assets," Mathematical Finance, Wiley Blackwell, vol. 7(3), pages 241-286, July.
    3. Gao, Bin & Huang, Jing-zhi & Subrahmanyam, Marti, 2000. "The valuation of American barrier options using the decomposition technique," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1783-1827, October.
    4. Jing-Zhi Huang & Marti G. Subrahmanyam & G. George Yu, 1999. "Pricing And Hedging American Options: A Recursive Integration Method," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 8, pages 219-239, World Scientific Publishing Co. Pte. Ltd..
    5. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," The Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-1250.
    6. Lee, Hangsuck & Ha, Hongjun & Kong, Byungdoo, 2024. "Pricing first-touch digitals with a multi-step double boundary and American barrier options," Finance Research Letters, Elsevier, vol. 59(C).
    7. 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.
    8. Andreas Andrikopoulos, 2010. "On the valuation of American exchange options: an analytical approximation," Applied Economics Letters, Taylor & Francis Journals, vol. 17(14), pages 1429-1435.
    9. Gerber, Hans U. & Shiu, Elias S. W., 1996. "Actuarial bridges to dynamic hedging and option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 18(3), pages 183-218, November.
    10. Bjerksund, Petter & Stensland, Gunnar, 1993. "Closed-form approximation of American options," Scandinavian Journal of Management, Elsevier, vol. 9(Supplemen), pages 87-99.
    11. Han, Heejae & Jeon, Junkee & Kang, Myungjoo, 2016. "Closed form valuation of American chained knock-in options," Finance Research Letters, Elsevier, vol. 17(C), pages 176-185.
    12. Lee, Hangsuck & Jeong, Himchan & Lee, Gaeun, 2023. "Valuing rebate options and equity-linked products," The North American Journal of Economics and Finance, Elsevier, vol. 68(C).
    13. Chung, San-Lin & Hung, Mao-Wei & Wang, Jr-Yan, 2010. "Tight bounds on American option prices," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 77-89, January.
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    More about this item

    Keywords

    American option; American barrier option; American exchange option; Rebate option; First-hitting time;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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