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Optimal exercise decision of American options under model uncertainty

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  • Tongseok Lim

Abstract

Given the marginal distribution information of the underlying asset price at two future times $T_1$ and $T_2$, we consider the problem of determining a model-free upper bound on the price of a class of American options that must be exercised at either $T_1$ or $T_2$. The model uncertainty consistent with the given marginal information is described as the martingale optimal transport problem. We show that any option exercise scheme associated with any market model that jointly maximizes the expected option payoff must be nonrandomized if the American option payoff satisfies a suitable convexity condition and the model-free price upper bound and its relaxed version coincide. The latter condition is desired to be removed under appropriate conditions on the cost and marginals.

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  • Tongseok Lim, 2023. "Optimal exercise decision of American options under model uncertainty," Papers 2310.14473, arXiv.org, revised Nov 2023.
    • Handle: RePEc:arx:papers:2310.14473
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    References listed on IDEAS

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    1. Erhan Bayraktar & Zhou Zhou, 2015. "Arbitrage, hedging and utility maximization using semi-static trading strategies with American options," Papers 1502.06681, arXiv.org, revised Feb 2016.
    2. Erhan Bayraktar & Zhou Zhou, 2019. "No-Arbitrage and Hedging with Liquid American Options," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 468-486, May.
    3. Pierre Henry-Labordère & Nizar Touzi, 2016. "An explicit martingale version of the one-dimensional Brenier theorem," Finance and Stochastics, Springer, vol. 20(3), pages 635-668, July.
    4. A. Galichon & P. Henry-Labord`ere & N. Touzi, 2014. "A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options," Papers 1401.3921, arXiv.org.
    5. Erhan Bayraktar & Yu-Jui Huang & Zhou Zhou, 2013. "On hedging American options under model uncertainty," Papers 1309.2982, arXiv.org, revised Apr 2015.
    6. Alfred Galichon & Pierre Henri-Labordère & Nizar Touzi, 2014. "A stochastic control approach to No-Arbitrage bounds given marginals, with an application to Lookback options," Post-Print hal-03460952, HAL.
    7. Erhan Bayraktar & Zhou Zhou, 2017. "Super-Hedging American Options With Semi-Static Trading Strategies Under Model Uncertainty," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(06), pages 1-10, September.
    8. Alfred Galichon & Pierre Henri-Labordère & Nizar Touzi, 2014. "A stochastic control approach to No-Arbitrage bounds given marginals, with an application to Lookback options," SciencePo Working papers Main hal-03460952, HAL.
    9. Alfred Galichon & Pierre Henri-Labordère & Nizar Touzi, 2014. "A stochastic control approach to No-Arbitrage bounds given marginals, with an application to Lookback options," SciencePo Working papers hal-03460952, HAL.
    10. Anna Aksamit & Shuoqing Deng & Jan Obłój & Xiaolu Tan, 2019. "The robust pricing–hedging duality for American options in discrete time financial markets," Mathematical Finance, Wiley Blackwell, vol. 29(3), pages 861-897, July.
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