Model-Independent Pricing of Asian Options via Optimal Martingale Transport

TL;DR

This paper develops a model-independent framework for pricing Asian options by characterizing optimal martingale transports, providing geometric insights and solutions for discrete and continuous averaging scenarios.

Contribution

It introduces geometric characterizations of optimal martingale transports for Asian options, extending to both discrete and continuous time cases with multiple marginals.

Findings

Optimal martingale transport solutions for Asian options.

Geometric characterizations of pricing bounds.

Connections between discrete and continuous models.

Abstract

In this article we discuss the problem of calculating optimal model-independent (robust) bounds for the price of Asian options with discrete and continuous averaging. We will give geometric characterisations of the maximising and the minimising pricing model for certain types of Asian options in discrete and continuous time. In discrete time the problem is reduced to finding the optimal martingale transport for the cost function $|x+y|$. In the continuous time case we consider the cases with one and two given marginals. We describe the maximising models in both of these cases as well as the minimising model in the one-marginal case and relate the two-marginals case to the discrete time problem with two marginals.