Probabilistic Limit Order Book Forecasting with Conditional Diffusion Models

Paper: arXiv 2610.25495

Authors: Junyu Chen, Franklin Liu, Moshu Xu, Lijian Yang

Abstract

Modeling limit order book (LOB) dynamics is central to market forecasting and execution-strategy evaluation. While diffusion models achieve strong empirical performance, existing LOB snapshot models typically lack a learned recurrent encoder and formal statistical guarantees. We introduce LOBGrad, a conditional DDPM framework for probabilistic LOB forecasting that combines an autoregressive RNN encoder with a diffusion-based generator. In particular, we establish an excess-risk oracle inequality for the one-step DDPM noise-prediction objective under exponential mixing and regularity assumptions. We further show that, under contractive dynamics, the dependence on the conditioning-window length can be reduced to a dependence on the latent-state dimension. Experiments on BTC/USDT, GOOGL, and META show that LOBGrad improves on its encoder-free diffusion ablation across all reported queue metrics and obtains competitive results against other baselines. It also reproduces the key stylized facts of LOB microstructure, and yields reasonably calibrated queue-based predictive intervals. A stylized downstream task illustrates the potential value of the generated forecasts.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a sophisticated mathematical framework for LOB forecasting, combining recurrent neural networks with diffusion models, and provides formal statistical guarantees. The empirical validation on real-world financial data (crypto and equities) demonstrates strong performance and addresses key stylized facts, indicating a robust methodology. The novelty lies in integrating an autoregressive RNN encoder into a conditional DDPM for LOB forecasting, along with theoretical contributions regarding excess-risk oracle inequality.

Research Flowchart

  flowchart TD
    A[Research Goal: Probabilistic LOB Forecasting] --> B{Key Methodology: LOBGrad Framework};
    B --> C{Inputs: LOB Data (BTC/USDT, GOOGL, META)};
    C --> D[Computational Process: RNN Encoder + Conditional Diffusion Generator];
    D --> E{Theoretical Contributions: Excess-Risk Oracle Inequality};
    E --> F[Key Findings: Improved Performance, Stylized Facts, Calibrated Intervals];
    F --> G[Outcome: Potential for Downstream Task Value];