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Path-dependent game options with Asian features

Author

Listed:
  • Guo, Peidong
  • Zhang, Jizhou
  • Wang, Qian

Abstract

The game option is a special American option, where the option seller has the early exercise right as well as the buyer. The purpose of this paper is to examine the pricing behaviors of a call game option with a floating strike, where the payoff of the option depends on the geometric average value of the underlying assets over the life of the option(i.e., the game option with the Asian feature). We obtain the integral expression of option pricing formula and provide the integral expression for the penalties paid by the option seller. In addition, we derive optimal exercise strategies and continuation regions of options. Finally, the influence of relevant parameters on liquidated damages is analyzed through numerical simulation.

Suggested Citation

  • Guo, Peidong & Zhang, Jizhou & Wang, Qian, 2020. "Path-dependent game options with Asian features," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    • Handle: RePEc:eee:chsofr:v:141:y:2020:i:c:s0960077920308055
    DOI: 10.1016/j.chaos.2020.110412
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    References listed on IDEAS

    as
    1. Ahmadian, D. & Ballestra, L.V., 2020. "Pricing geometric Asian rainbow options under the mixed fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    2. Zaevski, Tsvetelin S., 2020. "Discounted perpetual game put options," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    3. 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.
    4. Le, Nhat-Tan & Dang, Duy-Minh, 2017. "Pricing American-style Parisian down-and-out call options," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 330-347.
    5. Roxana Dumitrescu & Marie-Claire Quenez & Agn`es Sulem, 2015. "Game options in an imperfect market with default," Papers 1511.09041, arXiv.org, revised Jul 2017.
    6. Andreas Kyprianou, 2004. "Some calculations for Israeli options," Finance and Stochastics, Springer, vol. 8(1), pages 73-86, January.
    7. Xingchun Wang, 2020. "Analytical valuation of Asian options with counterparty risk under stochastic volatility models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(3), pages 410-429, March.
    8. Gao, Rong & Wu, Wei & Lang, Chao & Lang, Liying, 2020. "Geometric Asian barrier option pricing formulas of uncertain stock model," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    9. Peidong Guo & Qihong Chen & Xicai Guo & Yue Fang, 2014. "Path-dependent game options: a lookback case," Review of Derivatives Research, Springer, vol. 17(1), pages 113-124, April.
    10. 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.
    11. Wang, Xingchun, 2020. "Valuation of Asian options with default risk under GARCH models," International Review of Economics & Finance, Elsevier, vol. 70(C), pages 27-40.
    12. Zaevski, Tsvetelin S., 2020. "Discounted perpetual game call options," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    13. Madi, Sofiane & Cherif Bouras, Mohamed & Haiour, Mohamed & Stahel, Andreas, 2018. "Pricing of American options, using the Brennan–Schwartz algorithm based on finite elements," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 846-852.
    14. Zhang, Sumei & Gao, Xiong, 2019. "An asymptotic expansion method for geometric Asian options pricing under the double Heston model," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 1-9.
    15. Alet Roux, 2016. "Pricing And Hedging Game Options In Currency Models With Proportional Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(07), pages 1-25, November.
    16. Christoph Kühn & Andreas E. Kyprianou, 2007. "Callable Puts As Composite Exotic Options," Mathematical Finance, Wiley Blackwell, vol. 17(4), pages 487-502, October.
    17. Yuri Kifer, 2006. "Error estimates for binomial approximations of game options," Papers math/0607123, arXiv.org.
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    More about this item

    Keywords

    Game options; Asian features; American options; Path dependent;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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