First order Martingale model risk and semi-static hedging

TL;DR

This paper explores the impact of model risk on semi-static hedging strategies within a martingale framework, providing explicit solutions and analyzing robustness under Wasserstein metrics.

Contribution

It extends previous work by incorporating semi-static hedging into distributionally robust model risk analysis in Wasserstein spaces.

Findings

Explicit characterizations of first-order optimal semi-static hedging strategies.

Analysis of model risk robustness using Wasserstein and adapted Wasserstein metrics.

Extension of prior sensitivity results to include semi-static hedging strategies.

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.