Robust Pricing and Hedging around the Globe

TL;DR

This paper develops a duality framework for robust pricing and hedging of various options using martingale optimal transport, providing explicit strategies and proving strong duality for a broad class of payoffs.

Contribution

It introduces a duality approach for robust option pricing with cdlg processes, including explicit superhedging strategies and strong duality results.

Findings

Proves strong duality for a wide class of payoffs.

Constructs explicit superhedging strategies.

Includes American, Asian, Bermudan, and European options.

Abstract

We consider the martingale optimal transport duality for c\`adl\`ag processes with given initial and terminal laws. Strong duality and existence of dual optimizers (robust semi-static superhedging strategies) are proved for a class of payoffs that includes American, Asian, Bermudan, and European options with intermediate maturity. We exhibit an optimal superhedging strategy for which the static part solves an auxiliary problem and the dynamic part is given explicitly in terms of the static part.