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Pricing cancellable American put options on the finite time horizon

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  • Tsvetelin S. Zaevski

Abstract

The purpose of this paper is to present a numerical approach for pricing cancellable American put options, also known as game or Israeli options, on the finite time horizon. These options generalize the concept of American derivatives adding an early exercise right for the option's writer to the existing holder's right. The writer has to pay a penalty amount above the usual option payment to use this right. We first obtain the shape of the optimal regions for both participants. Then we approximate the optimal exercise boundaries maximizing the option's writer and holder financial expectations using some first exit properties of the Brownian motion. We also construct an efficient pricing algorithm based on these boundaries. A semiclosed form formula is derived when the underlying asset starts above the strike.

Suggested Citation

  • Tsvetelin S. Zaevski, 2022. "Pricing cancellable American put options on the finite time horizon," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(7), pages 1284-1303, July.
    • Handle: RePEc:wly:jfutmk:v:42:y:2022:i:7:p:1284-1303
    DOI: 10.1002/fut.22331
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    References listed on IDEAS

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    1. Zaevski, Tsvetelin S., 2020. "Discounted perpetual game put options," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    2. Gunter H Meyer, 2016. "A PDE View of Games Options," Research Paper Series 369, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Andreas Kyprianou, 2004. "Some calculations for Israeli options," Finance and Stochastics, Springer, vol. 8(1), pages 73-86, January.
    4. S. C. P. Yam & S. P. Yung & W. Zhou, 2014. "Game Call Options Revisited," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 173-206, January.
    5. Zaevski, Tsvetelin S., 2020. "Discounted perpetual game call options," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    6. Christoph Kühn & Andreas E. Kyprianou, 2007. "Callable Puts As Composite Exotic Options," Mathematical Finance, Wiley Blackwell, vol. 17(4), pages 487-502, October.
    7. Atsuo Suzuki & Katsushige Sawaki, 2007. "The Pricing Of Perpetual Game Put Options And Optimal Boundaries," World Scientific Book Chapters, in: Tadashi Dohi & Shunji Osaki & Katsushige Sawaki (ed.), Recent Advances In Stochastic Operations Research, chapter 12, pages 175-187, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Qi Zhang & Qi Wang & Ping Zuo & Hongbo Du & Fangfang Wu, 2023. "Projection and Contraction Method for Pricing American Bond Options," Mathematics, MDPI, vol. 11(22), pages 1-13, November.
    2. 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).
    3. Yan, Dong & Lin, Sha & Hu, Zhihao & Yang, Ben-Zhang, 2022. "Pricing American options with stochastic volatility and small nonlinear price impact: A PDE approach," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    4. Tsvetelin S. Zaevski, 2024. "Quadratic American Strangle Options in Light of Two-Sided Optimal Stopping Problems," Mathematics, MDPI, vol. 12(10), pages 1-27, May.

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