Generative Ornstein-Uhlenbeck Markets via Geometric Deep Learning
This work addresses financial modeling challenges for quantitative analysts by providing a flexible, assumption-free approach to market dynamics, though it appears incremental as it builds on existing geometric deep learning frameworks.
The paper tackles the problem of approximating both market price and log return distributions simultaneously using a single machine learning model, achieving universal approximation guarantees for conditional distributions and contingent claims with Lipschitz payoff functions.
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.