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Recombining tree approximations for Game Options in Local Volatility models

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  • Benjamin Gottesman Berdah

Abstract

In this paper we introduce a numerical method for optimal stopping in the framework of one dimensional diffusion. We use the Skorokhod embedding in order to construct recombining tree approximations for diffusions with general coefficients. This technique allows us to determine convergence rates and construct nearly optimal stopping times which are optimal at the same rate. Finally, we demonstrate the efficiency of our scheme with several examples of game options.

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  • Benjamin Gottesman Berdah, 2020. "Recombining tree approximations for Game Options in Local Volatility models," Papers 2007.02323, arXiv.org, revised Jul 2020.
    • Handle: RePEc:arx:papers:2007.02323
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    References listed on IDEAS

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    1. Andreas Kyprianou, 2004. "Some calculations for Israeli options," Finance and Stochastics, Springer, vol. 8(1), pages 73-86, January.
    2. Christoph Kühn & Andreas E. Kyprianou, 2007. "Callable Puts As Composite Exotic Options," Mathematical Finance, Wiley Blackwell, vol. 17(4), pages 487-502, October.
    3. 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.
    4. Yoshio Ohtsubo, 1986. "Optimal Stopping in Sequential Games With or Without a Constraint of Always Terminating," Mathematics of Operations Research, INFORMS, vol. 11(4), pages 591-607, November.
    5. 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.
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