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

Paper: arXiv 2610.21081

Authors: Arshia Abolghasemi, Seyed Reza Tavakoli, Parsa Naderi, Nazanin Mirzaei, Behrad Jahani, Saba Yousefzadeh, Tahereh Javaheri, Mohammad Hosein Rohban, Gholamali Aminian, Ali Habibnia

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 $h_t(r)$ 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.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly novel and mathematically sophisticated approach to LOB trend prediction by incorporating heavy-tailed noise into score-matching diffusion models. The empirical validation on real-world LOB data, including stress diagnostics and a transfer study, demonstrates strong rigor. The provided code link further enhances reproducibility.

Research Flowchart

  flowchart TD
    A[Research Goal: Robust LOB Trend Prediction with Heavy-Tailed Noise] --> B{Key Methodology: Training-Only Score-Matching}
    B --> C{Noise Corruption Laws: Jump-Lévy & Clipped α-stable SDEs}
    C --> D[Inputs: Coinbase LOB Data (BTC/altcoin), Feishu A-share Transfer Data]
    D --> E{Computational Process: StochLOB Framework Training}
    E --> F[Outcomes: Improved Tail-Window Stress Diagnostics, Competitive Performance]
    F --> G[Interpretation: Score Target radial factor = posterior expected corruption precision]

Cited References (54)

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6. Limit Order Books (2013) — link
7. The Price Impact of Order Book Events (2014) — link
8. Deep Order Flow Imbalance: Extracting Alpha at Multiple Horizons from the Limit Order Book (2023) — link

2 of 54 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.