Model Risk Static-Hedging a Constrained Distributionally Robust Optimization approach

TL;DR

This paper advances the understanding of model risk and distributionally robust optimization by developing static hedging strategies under complex constraints, providing new sensitivity formulas and measure construction methods.

Contribution

It introduces a novel approach to static hedging with second-period vanilla options under marginal and martingale constraints, extending previous work with new theoretical tools.

Findings

Derived closed-form sensitivity formulas.

Constructed measure families satisfying constraints.

Characterized hedging strategies for real-valued processes.

Abstract

We investigate model risk and distributionally robust optimization (DRO) under marginal and martingale constraints. Building on our previous work, we address the previously open case of static hedging with second-period maturity vanilla options and hedging strategies involving a vanilla payoff. We also extend recent sensitivity results to settings where admissible models must satisfy a martingale coupling constraint. Our approach relies on a weak implicit function theorem argument to construct families of measures satisfying the prescribed constraints. We derive closed-form sensitivity formulas and characterize the corresponding hedging strategies when the underlying process is real-valued.