A diffusion-based generative model for financial time series via geometric Brownian motion

TL;DR

This paper introduces a diffusion-based generative model for financial time series that integrates geometric Brownian motion, capturing key market phenomena more accurately than traditional models.

Contribution

It develops a novel diffusion framework incorporating GBM into the noising process, using a Transformer-based architecture for improved financial data generation.

Findings

Reproduces heavy-tailed return distributions

Captures volatility clustering effectively

Models leverage effect more realistically

Abstract

We propose a novel diffusion-based generative framework for financial time series that incorporates geometric Brownian motion (GBM), the foundation of the Black--Scholes theory, into the forward noising process. Unlike standard score-based models that treat price trajectories as generic numerical sequences, our method injects noise proportionally to asset prices at each time step, reflecting the heteroskedasticity observed in financial time series. By accurately balancing the drift and diffusion terms, we show that the resulting log-price process reduces to a variance-exploding stochastic differential equation, aligning with the formulation in score-based generative models. The reverse-time generative process is trained via denoising score matching using a Transformer-based architecture adapted from the Conditional Score-based Diffusion Imputation (CSDI) framework. Empirical evaluations on historical stock data demonstrate that our model reproduces key stylized facts heavy-tailed return distributions, volatility clustering, and the leverage effect more realistically than conventional diffusion models.