First order Martingale model risk and semi-static hedging

Nathan Sauldubois; Nizar Touzi

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arXiv · 2410.06906

First order Martingale model risk and semi-static hedging

Nathan Sauldubois·Nizar Touzi

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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. 2024-10-09. First order Martingale model risk and semi-static hedging. https://arxiv.org/abs/2410.06906

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