Neural Options Pricing

TL;DR

This paper introduces a neural SDE-based approach for option pricing that leverages the Wasserstein distance for training, allowing flexible modeling of underlying processes and providing theoretical bounds on pricing errors.

Contribution

It proposes a novel neural SDE framework with Wasserstein distance-based training for arbitrage-free option pricing, relaxing traditional assumptions.

Findings

Neural SDEs can approximate complex price processes.

Wasserstein distance effectively trains neural SDE models.

Theoretical bounds relate pricing error to Wasserstein distance.

Abstract

This research investigates pricing financial options based on the traditional martingale theory of arbitrage pricing applied to neural SDEs. We treat neural SDEs as universal It\^o process approximators. In this way we can lift all assumptions on the form of the underlying price process, and compute theoretical option prices numerically. We propose a variation of the SDE-GAN approach by implementing the Wasserstein distance metric as a loss function for training. Furthermore, it is conjectured that the error of the option price implied by the learnt model can be bounded by the very Wasserstein distance metric that was used to fit the empirical data.