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A PDE View of Games Options

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  • Gunter H Meyer

    (Georgia Institute of Technology)

Abstract

Game put and call options are defined and solved with an approach based on differential equations which completely bypasses their usual treatment as stochastic Dynkin games. The view is taken that when the writer of the option plans to cancel an American put or call at particular values of the underlying asset, then those assets function as twosided barriers for the cancellable option. A game option results when the location of the barriers is chosen such that the value of the option is minimized. With elementary maximum and comparison principles from differential equations, optimal cancellation strategies can be readily found and interpreted graphically for perpetual options. An analogous treatment appears possible for finite time game options. An application of the approach to an American game CEV call and to callable stock loans is described.

Suggested Citation

  • Gunter H Meyer, 2016. "A PDE View of Games Options," Research Paper Series 369, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:369
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    File URL: https://www.uts.edu.au/sites/default/files/qfr-archive-03/QFR-rp369.pdf
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    References listed on IDEAS

    as
    1. Marta Leniec & Kristoffer Glover & Erik Ekström, 2017. "Dynkin games with heterogeneous beliefs," Published Paper Series 2017-2, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    2. Erik Ekström, 2006. "Properties of game options," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(2), pages 221-238, May.
    3. Jianming Xia & Xun Yu Zhou, 2007. "Stock Loans," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 307-317, April.
    4. Andreas Kyprianou, 2004. "Some calculations for Israeli options," Finance and Stochastics, Springer, vol. 8(1), pages 73-86, January.
    5. 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.
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    Cited by:

    1. 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.
    2. Zaevski, Tsvetelin S., 2020. "Discounted perpetual game call options," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).

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