Robust pricing and hedging of options on multiple assets and its numerics

TL;DR

This paper develops robust methods for pricing and hedging options on multiple assets using multi-marginal martingale optimal transport, introducing two numerical approaches and analyzing their convergence and performance.

Contribution

It introduces two novel numerical methods for multi-asset option pricing via martingale optimal transport, with convergence proofs and performance comparisons.

Findings

Discretisation and linear programming method is effective for primal problems.

Deep neural network approach is viable for dual problems.

Additional market information refines no-arbitrage bounds.

Abstract

We consider robust pricing and hedging for options written on multiple assets given market option prices for the individual assets. The resulting problem is called the multi-marginal martingale optimal transport problem. We propose two numerical methods to solve such problems: using discretisation and linear programming applied to the primal side and using penalisation and deep neural networks optimisation applied to the dual side. We prove convergence for our methods and compare their numerical performance. We show how adding further information about call option prices at additional maturities can be incorporated and narrows down the no-arbitrage pricing bounds. Finally, we obtain structural results for the case of the payoff given by a weighted sum of covariances between the assets.