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 α-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 ht(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 https://github.com/ArshiAbolghasemi/Penny.
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BibTeX
@misc{abolghasemi2026stochlob,
title = {{StochLOB: Heavy-Tailed Score Matching for Robust Limit Order Book Trend Prediction}},
author = {Arshia Abolghasemi and Seyed Reza Tavakoli and Parsa Naderi and Nazanin Mirzaei and Behrad Jahani and Saba Yousefzadeh and Tahereh Javaheri and Mohammad Hosein Rohban and Gholamali Aminian and Ali Habibnia},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21081},
eprint = {2610.21081},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21081},
}
RIS
TY - UNPB
TI - StochLOB: Heavy-Tailed Score Matching for Robust Limit Order Book Trend Prediction
AU - Arshia Abolghasemi
AU - Seyed Reza Tavakoli
AU - Parsa Naderi
AU - Nazanin Mirzaei
AU - Behrad Jahani
AU - Saba Yousefzadeh
AU - Tahereh Javaheri
AU - Mohammad Hosein Rohban
AU - Gholamali Aminian
AU - Ali Habibnia
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.21081
UR - https://arxiv.org/abs/2610.21081
AB - 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 α-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 https://github.com/ArshiAbolghasemi/Penny.
ER -