A diffusion-based generative model for financial time series via geometric Brownian motion
This work addresses the challenge of generating accurate financial data for applications in risk management and trading, though it is incremental as it builds on existing diffusion models by adapting them to domain-specific heteroskedasticity.
The authors tackled the problem of generating realistic financial time series by proposing a diffusion-based generative model that incorporates geometric Brownian motion into the noising process, resulting in improved reproduction of stylized facts like heavy-tailed returns and volatility clustering compared to conventional methods.
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.