[2604.00195] Lévy-Flow Models: Heavy-Tail-Aware Normalizing Flows for Financial Risk Management

Computer Science > Machine Learning arXiv:2604.00195 (cs) [Submitted on 31 Mar 2026] Title:Lévy-Flow Models: Heavy-Tail-Aware Normalizing Flows for Financial Risk Management Authors:Rachid Drissi View a PDF of the paper titled L\'evy-Flow Models: Heavy-Tail-Aware Normalizing Flows for Financial Risk Management, by Rachid Drissi View PDF HTML (experimental) Abstract:We introduce Lévy-Flows, a class of normalizing flow models that replace the standard Gaussian base distribution with Lévy process-based distributions, specifically Variance Gamma (VG) and Normal-Inverse Gaussian (NIG). These distributions naturally capture heavy-tailed behavior while preserving exact likelihood evaluation and efficient reparameterized sampling. We establish theoretical guarantees on tail behavior, showing that for regularly varying bases the tail index is preserved under asymptotically linear flow transformations, and that identity-tail Neural Spline Flow architectures preserve the base distribution's tail shape exactly outside the transformation region. Empirically, we evaluate on S&P 500 daily returns and additional assets, demonstrating substantial improvements in density estimation and risk calibration. VG-based flows reduce test negative log-likelihood by 69% relative to Gaussian flows and achieve exact 95% VaR calibration, while NIG-based flows provide the most accurate Expected Shortfall estimates. These results show that incorporating Lévy process structure into normalizing flows yields...