Bounds on Multi-asset Derivatives via Neural Networks

TL;DR

This paper introduces a neural network-based method to compute tight bounds on multi-asset derivative prices using related payoff information, enhancing accuracy through additional constraints and optimal transport techniques.

Contribution

It presents a novel neural network approach for deriving bounds on multi-asset derivatives incorporating multiple constraints, extending prior optimal transport methods.

Findings

Adding constraints significantly tightens bounds.

Neural networks effectively approximate optimal couplings.

Method applies to various multi-asset derivatives.

Abstract

Using neural networks, we compute bounds on the prices of multi-asset derivatives given information on prices of related payoffs. As a main example, we focus on European basket options and include information on the prices of other similar options, such as spread options and/or basket options on subindices. We show that, in most cases, adding further constraints gives rise to bounds that are considerably tighter and discuss the maximizing/minimizing copulas achieving such bounds. Our approach follows the literature on constrained optimal transport and, in particular, builds on a recent paper by Eckstein and Kupper (2019, Appl. Math. Optim.).