Generative Ornstein-Uhlenbeck Markets via Geometric Deep Learning

TL;DR

This paper introduces a geometric deep learning model that can simultaneously approximate market prices and log returns, assuming they follow a generalized Ornstein-Uhlenbeck process, without prior assumptions on their dynamics.

Contribution

It demonstrates that the GDN model can universally approximate conditional distributions of market variables under minimal assumptions, extending prior work to financial markets.

Findings

Universal approximation guarantees for conditional distributions

Effective modeling of market prices and log returns

No prior assumptions on market dynamics required

Abstract

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 Kratsios and Papon (2022) 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.