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More on hedging American options under model uncertainty

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  • David Hobson
  • Anthony Neuberger

Abstract

The purpose of this note is to reconcile two different results concerning the model-free upper bound on the price of an American option, given a set of European option prices. Neuberger (2007, `Bounds on the American option') and Hobson and Neuberger (2016, `On the value of being American') argue that the cost of the cheapest super-replicating strategy is equal to the highest model-based price, where we search over all models which price correctly the given European options. Bayraktar, Huang and Zhou (2015, `On hedging American options under model uncertainty', SIAM J. Financial Math ematics) argue that the cost of the cheapest super-replicating strategy can strictly exceed the highest model-based price. We show that the reason for the difference in conclusion is that Bayraktar et al do not search over a rich enough class of models.

Suggested Citation

  • David Hobson & Anthony Neuberger, 2016. "More on hedging American options under model uncertainty," Papers 1604.02274, arXiv.org.
    • Handle: RePEc:arx:papers:1604.02274
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    References listed on IDEAS

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    1. Erhan Bayraktar & Yu-Jui Huang & Zhou Zhou, 2013. "On hedging American options under model uncertainty," Papers 1309.2982, arXiv.org, revised Apr 2015.
    2. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008, arXiv.org, revised Mar 2015.
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    Cited by:

    1. David Hobson & Dominykas Norgilas, 2019. "Robust bounds for the American put," Finance and Stochastics, Springer, vol. 23(2), pages 359-395, April.
    2. Anna Aksamit & Shuoqing Deng & Jan Obl'oj & Xiaolu Tan, 2016. "Robust pricing--hedging duality for American options in discrete time financial markets," Papers 1604.05517, arXiv.org, revised Apr 2017.
    3. David Hobson & Dominykas Norgilas, 2017. "Robust bounds for the American Put," Papers 1711.06466, arXiv.org, revised May 2018.
    4. 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.
    5. Cox, Alexander M.G. & Kinsley, Sam M., 2019. "Discretisation and duality of optimal Skorokhod embedding problems," Stochastic Processes and their Applications, Elsevier, vol. 129(7), pages 2376-2405.

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