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First order Martingale model risk and semi-static hedging

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  • Nathan Sauldubois
  • Nizar Touzi

Abstract

We investigate model risk distributionally robust sensitivities for functionals on the Wasserstein space when the underlying model is constrained to the martingale class and/or is subject to constraints on the first marginal law. Our results extend the findings of Bartl, Drapeau, Obloj \& Wiesel \cite{bartl2021sensitivity} and Bartl \& Wiesel \cite{bartlsensitivityadapted} by introducing the minimization of the distributionally robust problem with respect to semi-static hedging strategies. We provide explicit characterizations of the model risk (first order) optimal semi-static hedging strategies. The distributional robustness is analyzed both in terms of the adapted Wasserstein metric and the more relevant standard Wasserstein metric.

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  • Nathan Sauldubois & Nizar Touzi, 2024. "First order Martingale model risk and semi-static hedging," Papers 2410.06906, arXiv.org.
    • Handle: RePEc:arx:papers:2410.06906
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    References listed on IDEAS

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    1. Julio Backhoff-Veraguas & Daniel Bartl & Mathias Beiglböck & Manu Eder, 2020. "Adapted Wasserstein distances and stability in mathematical finance," Finance and Stochastics, Springer, vol. 24(3), pages 601-632, July.
    2. Julio Backhoff-Veraguas & Daniel Bartl & Mathias Beiglbock & Manu Eder, 2019. "Adapted Wasserstein Distances and Stability in Mathematical Finance," Papers 1901.07450, arXiv.org, revised May 2020.
    3. Ariel Neufeld & Matthew Ng Cheng En & Ying Zhang, 2024. "Robust SGLD algorithm for solving non-convex distributionally robust optimisation problems," Papers 2403.09532, arXiv.org.
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    Cited by:

    1. Ruslan Mirmominov & Johannes Wiesel, 2024. "A dynamic programming principle for multiperiod control problems with bicausal constraints," Papers 2410.23927, arXiv.org.

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