Neural Options Pricing
This addresses the problem of pricing options without restrictive assumptions for financial practitioners, though it appears incremental as it builds on existing SDE-GAN methods.
The research tackled pricing financial options by applying martingale theory to neural stochastic differential equations (SDEs) as universal approximators, eliminating assumptions on underlying price processes and computing theoretical prices numerically, with a proposed SDE-GAN variation using Wasserstein distance for training and a conjecture that pricing error can be bounded by this distance.
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 Itô 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.