Generative OrnsteinUhlenbeck Markets via Geometric Deep Learning

We consider the problem of simultaneously approximating the conditional distribution of market prices and their log returns with a single machine learning model. We show that an instance of the GDN model of [13] solves this problem without having prior assumptions on the market’s “clipped” log returns, other than that they follow a generalized Ornstein-Uhlenbeck process with a priori unknown dynamics. We provide universal approximation guarantees for these conditional distributions and contingent claims with a Lipschitz payoff function.