StochLOB: Heavy-Tailed Score Matching for Robust Limit Order Book Trend Prediction

Abstract:Score-based diffusion methods usually perturb data with Brownian Gaussian noise, corresponding to a light-tailed forward stochastic differential equation (SDE). For market time series this SDE can be a poor abstraction: limit order book (LOB) order flow is heavy-tailed, bursty, and occasionally jump-like. We study STOCHLOB, a training-only score-matching framework that changes the forward diffusion corruption law while leaving the deployed predictor deterministic. Instead of Brownian-only Gaussian corruption, the noising process uses two non-Gaussian SDE-inspired alternatives: jump-Lévy noise through a compound-Poisson variance mixture, and clipped $\alpha$-stable noise through a positive-stable Gaussian scale mixture. These corruptions inject finite jumps and heavy-tailed residuals into training without requiring reverse-time diffusion sampling at inference. The resulting score target has a useful interpretation: its radial factor $h_t(r)$ is the posterior expected corruption precision, so large residuals are weighted according to the latent corruption scale that most plausibly generated them. On chronologically held-out Coinbase LOB data, the proposed variants remain competitive on uncorrupted BTC and altcoin test horizons and improve several realized tail-window stress diagnostics. An exploratory Feishu A-share transfer study further tests whether the probability outputs remain usable under transaction costs and trading-rule constraints. Code and configuration files are available at this https URL.

32 pages, 5 figures. NeurIPS 2026 Workshop: AI for Stochastic Dynamics

Machine Learning (cs.LG); Trading and Market Microstructure (q-fin.TR); Machine Learning (stat.ML)

arXiv:2610.21081 [cs.LG]

(or arXiv:2610.21081v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.21081 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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