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Discounted perpetual game put options

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  • Zaevski, Tsvetelin S.

Abstract

The aim of this study is to explore the behavior of perpetual game put options, also known as cancellable puts. Their main characteristic is the opportunity of the buyer and the seller to exercise prematurely. If the seller decides to terminate the option, he obliges to pay a penalty amount above the normal option fee. We include also a discount factor that provides an advantage for earlier option exercising. We obtain the optimal moments for both participants to end the option promptly. This allows us to turn the option pricing problem to a first exit problem. We base our examination on financial instruments with random maturities. These instruments permit one of the partakers to maximize his expected future profit.

Suggested Citation

  • Zaevski, Tsvetelin S., 2020. "Discounted perpetual game put options," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    • Handle: RePEc:eee:chsofr:v:137:y:2020:i:c:s0960077920302587
    DOI: 10.1016/j.chaos.2020.109858
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    References listed on IDEAS

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    1. Baurdoux, Erik J. & Kyprianou, Andreas E., 2004. "Further calculations for Israeli options," LSE Research Online Documents on Economics 23916, London School of Economics and Political Science, LSE Library.
    2. Li, Chenxu & Ye, Yongxin, 2019. "Pricing and Exercising American Options: an Asymptotic Expansion Approach," Journal of Economic Dynamics and Control, Elsevier, vol. 107(C), pages 1-1.
    3. Anis Matoussi & Lambert Piozin & Dylan Possamai, 2012. "Second-order BSDEs with general reflection and game options under uncertainty," Papers 1212.0476, arXiv.org, revised Jan 2014.
    4. Andreas Kyprianou, 2004. "Some calculations for Israeli options," Finance and Stochastics, Springer, vol. 8(1), pages 73-86, January.
    5. Zaevski, Tsvetelin S., 2020. "Discounted perpetual game call options," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    6. Jan Kallsen & Christoph Kühn, 2004. "Pricing derivatives of American and game type in incomplete markets," Finance and Stochastics, Springer, vol. 8(2), pages 261-284, May.
    7. Lu, Xiaoping & Putri, Endah R.M., 2020. "A semi-analytic valuation of American options under a two-state regime-switching economy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    8. 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..
    9. Пигнастый, Олег & Koжевников, Георгий, 2019. "Распределенная Динамическая Pde-Модель Программного Управления Загрузкой Технологического Оборудования Производственной Линии [Distributed dynamic PDE-model of a program control by utilization of t," MPRA Paper 93278, University Library of Munich, Germany, revised 02 Feb 2019.
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    Citations

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    Cited by:

    1. Guo, Peidong & Zhang, Jizhou & Wang, Qian, 2020. "Path-dependent game options with Asian features," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. 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.
    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, 2023. "American strangle options with arbitrary strikes," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(7), pages 880-903, July.
    5. Deng, Guohe, 2020. "Pricing perpetual American floating strike lookback option under multiscale stochastic volatility model," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    6. Zaevski, Tsvetelin S., 2022. "Pricing discounted American capped options," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).

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    More about this item

    Keywords

    Game options; Cancellable puts; American style instruments; Optimal regions;
    All these keywords.

    JEL classification:

    • C57 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Econometrics of Games and Auctions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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