  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.
