Mathematical and Computational Finance Seminar

Diffusion models for time-series generation are typically trained with Gaussian perturbations, which may underrepresent rare but consequential extremes in financial data. Motivated by the heavy-tailed nature of financial time series, we investigate Lévy-Driven Diffusion for Time Series (TSLD), where Gaussian noise is replaced by Lévy α-stable perturbations in an attempt to better capture tail behavior while preserving temporal dynamics. However, we find that Lévy perturbations introduce substantial instability during training and do not consistently improve generative performance. Beyond distributional fit, we assess financial coherence by comparing generated samples against standard stylized facts, including heavy tails, volatility clustering, and weak linear autocorrelation.

 

More broadly, these results highlight the difficulty of evaluating generative models for financial time series. A model may be theoretically appealing from a distributional perspective while still failing to improve stability, temporal coherence, or downstream usefulness. This motivates the need for carefully designed benchmarks that go beyond visual inspection or marginal distribution matching.