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

Score-based diffusion methods typically perturb data with Gaussian noise induced by Brownian motion, corresponding to a light-tailed forward stochastic differential equation (SDE). For market time series, this SDE can be a poor abstraction because 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 during 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 most likely to have 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 transfer study using Feishu A-share data further examines whether StochLOB’s probability outputs remain useful for portfolio construction under transaction costs and trading-rule constraints. Code and configuration files are available at https://github.com/ArshiAbolghasemi/Penny.