Computation of Robust Option Prices via Structured Multi-Marginal Martingale Optimal Transport

TL;DR

This paper presents a new computational approach for efficiently solving multi-marginal martingale optimal transport problems, which are crucial for robust option pricing, by leveraging state space extension and entropic regularisation to handle large-scale problems.

Contribution

The authors develop a novel method that exploits sequential martingale structures and entropic regularisation, enabling fast computation of robust option prices with many marginals.

Findings

Successfully computes robust price bounds for lookback options.

Demonstrates efficiency in handling problems with many marginals.

Provides a practical framework for large-scale financial applications.

Abstract

We introduce an efficient computational framework for solving a class of multi-marginal martingale optimal transport problems, which includes many robust pricing problems of large financial interest. Such problems are typically computationally challenging due to the martingale constraint, however, by extending the state space we can identify them with problems that exhibit a certain sequential martingale structure. Our method exploits such structures in combination with entropic regularisation, enabling fast computation of optimal solutions and allowing us to solve problems with a large number of marginals. We demonstrate the method by using it for computing robust price bounds for different options, such as lookback options and Asian options.