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Superhedging duality for multi-action options under model uncertainty with information delay

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  • Anna Aksamit
  • Ivan Guo
  • Shidan Liu
  • Zhou Zhou

Abstract

We consider the superhedging price of an exotic option under nondominated model uncertainty in discrete time in which the option buyer chooses some action from an (uncountable) action space at each time step. By introducing an enlarged space we reformulate the superhedging problem for such an exotic option as a problem for a European option, which enables us to prove the pricing-hedging duality. Next, we present a duality result that, when the option buyers action is observed by the seller up to $l$ periods later, the superhedging price equals the model-based price where the option buyer has the power to look into the future for $l$ periods.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:2111.14502
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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.
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    7. Sebastian Herrmann & Florian Stebegg, 2017. "Robust Pricing and Hedging around the Globe," Papers 1707.08545, arXiv.org, revised Apr 2019.
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    13. 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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    Cited by:

    1. Alexander M. G. Cox & Annemarie M. Grass, 2023. "Robust option pricing with volatility term structure -- An empirical study for variance options," Papers 2312.09201, arXiv.org.
    2. Tongseok Lim, 2023. "Replication of financial derivatives under extreme market models given marginals," Papers 2307.00807, arXiv.org.

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