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Super-Hedging American Options With Semi-Static Trading Strategies Under Model Uncertainty

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  • ERHAN BAYRAKTAR

    (Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109, USA)

  • ZHOU ZHOU

    (Institute for Mathematics and its Applications, University of Minnesota, 207 Church Street, SE, Minneapolis, MN 55455, USA)

Abstract

We consider the super-hedging price of an American option in a discrete-time market in which stocks are available for dynamic trading and European options are available for static trading. We show that the super-hedging price π is given by the supremum over the prices of the American option under randomized models. That is, π =sup(ci,Qi)i∑iciϕQi, where ci ∈ ℝ+ and the martingale measure Qi are chosen such that ∑ici = 1 and ∑iciQi prices the European options correctly, and ϕQi is the price of the American option under the model Qi. Our result generalizes the example given in Hobson & Neuberger (2016) that the highest model-based price can be considered as a randomization over models.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:20:y:2017:i:06:n:s0219024917500364
    DOI: 10.1142/S0219024917500364
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    References listed on IDEAS

    as
    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. Erhan Bayraktar & Yu-Jui Huang & Zhou Zhou, 2013. "On hedging American options under model uncertainty," Papers 1309.2982, arXiv.org, revised Apr 2015.
    4. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008, arXiv.org, revised Mar 2015.
    5. David Hobson & Anthony Neuberger, 2017. "Model uncertainty and the pricing of American options," Finance and Stochastics, Springer, vol. 21(1), pages 285-329, January.
    6. David Hobson & Anthony Neuberger, 2016. "More on hedging American options under model uncertainty," Papers 1604.02274, arXiv.org.
    7. David Hobson & Anthony Neuberger, 2016. "On the value of being American," Papers 1604.02269, arXiv.org.
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    Citations

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    Cited by:

    1. Anna Aksamit & Ivan Guo & Shidan Liu & Zhou Zhou, 2021. "Superhedging duality for multi-action options under model uncertainty with information delay," Papers 2111.14502, arXiv.org, revised Nov 2023.
    2. Valeriane Jokhadze & Wolfgang M. Schmidt, 2020. "Measuring Model Risk In Financial Risk Management And Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(02), pages 1-37, April.
    3. Matteo Burzoni & Marco Frittelli & Zhaoxu Hou & Marco Maggis & Jan Obłój, 2019. "Pointwise Arbitrage Pricing Theory in Discrete Time," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 1034-1057, August.
    4. Mun-Chol Kim & Song-Chol Ryom, 2022. "Pathwise superhedging under proportional transaction costs," Mathematics and Financial Economics, Springer, volume 16, number 4, December.
    5. 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.
    6. Paolo Di Tella & Martin Haubold & Martin Keller-Ressel, 2017. "Semi-Static Variance-Optimal Hedging in Stochastic Volatility Models with Fourier Representation," Papers 1709.05527, arXiv.org.
    7. Alessandro Doldi & Marco Frittelli, 2020. "Entropy Martingale Optimal Transport and Nonlinear Pricing-Hedging Duality," Papers 2005.12572, arXiv.org, revised Sep 2021.
    8. 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.
    9. Alessandro Doldi & Marco Frittelli & Emanuela Rosazza Gianin, 2024. "On entropy martingale optimal transport theory," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 1-42, June.
    10. Christopher W. Miller, 2016. "A Duality Result for Robust Optimization with Expectation Constraints," Papers 1610.01227, arXiv.org.
    11. Tongseok Lim, 2023. "Optimal exercise decision of American options under model uncertainty," Papers 2310.14473, arXiv.org, revised Nov 2023.

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