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Discounted perpetual game call options

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  • Zaevski, Tsvetelin S.

Abstract

The purpose of this paper is to examine the problem of pricing discounted perpetual game call options. In addition to the properties of the American options, the game options give the seller the right to cancel the contract at some chosen from him moment. As a compensation for this, he has to pay some amount above the usual payment. We assume that this penalty payment is a constant. We examine the case without maturity – the exercise can be made in every future moment. We first derive the optimal exercise regions for the buyer and the seller and then calculate the fair option price. Our approach is based on some American style derivatives with a stochastic maturity date.

Suggested Citation

  • Zaevski, Tsvetelin S., 2020. "Discounted perpetual game call options," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    • Handle: RePEc:eee:chsofr:v:131:y:2020:i:c:s0960077919304552
    DOI: 10.1016/j.chaos.2019.109503
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    References listed on IDEAS

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    1. Zaevski, Tsvetelin S., 2019. "A new form of the early exercise premium for American type derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 338-340.
    2. Pereira, Paulo J. & Rodrigues, Artur, 2019. "Investing in a random start American option under competition," Finance Research Letters, Elsevier, vol. 28(C), pages 388-397.
    3. Klimsiak, Tomasz & Rozkosz, Andrzej & Ziemkiewicz, Bartosz, 2016. "Valuing American options by simulation: A BSDEs approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 123(C), pages 1-18.
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    6. Gunter H Meyer, 2016. "A PDE View of Games Options," Research Paper Series 369, Quantitative Finance Research Centre, University of Technology, Sydney.
    7. Andreas Kyprianou, 2004. "Some calculations for Israeli options," Finance and Stochastics, Springer, vol. 8(1), pages 73-86, January.
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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, 2023. "American strangle options with arbitrary strikes," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(7), pages 880-903, July.
    3. Deng, Guohe, 2020. "Pricing perpetual American floating strike lookback option under multiscale stochastic volatility model," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    4. Zaevski, Tsvetelin S., 2022. "Pricing discounted American capped options," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    5. 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.
    6. Zaevski, Tsvetelin S., 2020. "Discounted perpetual game put options," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    7. 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).
    8. Andrew Kumiega & Greg Sterijevski & Eric Wills, 2024. "Black–Scholes 50 Years Later: Has the Outperformance of Passive Option Strategies Finally Faded?," IJFS, MDPI, vol. 12(4), pages 1-17, November.

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    More about this item

    Keywords

    Game options; Israeli options; American options; Exercise regions; Optimal boundaries;
    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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