Relevance of Wasserstein Distance for Path-Dependent Option Pricing

Determine whether minimizing the Wasserstein distance between learned and target payoff distributions is an adequate evaluation or training criterion for distributional reinforcement learning models that price path-dependent options such as arithmetic Asian call options under the risk-neutral measure, specifically with respect to capturing financially critical aspects including tail behavior and extreme quantile accuracy of the conditional payoff distribution.

Background

The paper adopts distributional reinforcement learning to learn full conditional payoff distributions for path-dependent options and notes that the distributional Bellman operator is a contraction under the Wasserstein metric. Despite this theoretical property, the authors question whether Wasserstein distance is practically sufficient as an evaluation criterion for financial tasks where tail behavior and extreme quantiles are crucial.

They highlight that, to their knowledge, there has been no thorough paper assessing this limitation in the context of finance, especially for path-dependent option pricing, and therefore call for a targeted investigation into the practical adequacy of Wasserstein-based objectives and metrics for such applications.