Limit Order Book Event Stream Prediction with Diffusion Model

Paper: arXiv 2412.09631

Abstract

Limit order book (LOB) is a dynamic, event-driven system that records real-time market demand and supply for a financial asset in a stream flow. Event stream prediction in LOB refers to forecasting both the timing and the type of events. The challenge lies in modeling the time-event distribution to capture the interdependence between time and event type, which has traditionally relied on stochastic point processes. However, modeling complex market dynamics using stochastic processes, e.g., Hawke stochastic process, can be simplistic and struggle to capture the evolution of market dynamics. In this study, we present LOBDIF (LOB event stream prediction with diffusion model), which offers a new paradigm for event stream prediction within the LOB system. LOBDIF learns the complex time-event distribution by leveraging a diffusion model, which decomposes the time-event distribution into sequential steps, with each step represented by a Gaussian distribution. Additionally, we propose a denoising network and a skip-step sampling strategy. The former facilitates effective learning of time-event interdependence, while the latter accelerates the sampling process during inference. By introducing a diffusion model, our approach breaks away from traditional modeling paradigms, offering novel insights and providing an effective and efficient solution for learning the time-event distribution in order streams within the LOB system. Extensive experiments using real-world data from the limit order books of three widely traded assets confirm that LOBDIF significantly outperforms current state-of-the-art methods.

Complexity vs Empirical Score

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

Why this score: The paper employs advanced stochastic modeling with diffusion models and Gaussian distributions, indicating high mathematical complexity. It also demonstrates empirical rigor through extensive experiments on real-world limit order book data from three assets, outperforming state-of-the-art methods, making it well-suited for practical implementation.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Model Time-Event Distribution<br>in Limit Order Books"] --> B["Methodology: LOBDIF<br>Diffusion Model Approach"]
  
  B --> C{"Key Components"}
  C --> D["1. Denoising Network<br>Learns Time-Event Interdependence"]
  C --> E["2. Skip-Step Sampling<br>Accelerates Inference"]
  
  D --> F["Input: Real-World LOB Data<br>from 3 High-Frequency Traded Assets"]
  E --> F
  
  F --> G["Computational Process<br>Sequential Denoising<br>Time-Event Distribution Prediction"]
  
  G --> H["Key Findings & Outcomes"]
  H --> I["Significantly Outperforms<br>State-of-the-Art Methods"]
  H --> J["Effective & Efficient<br>Time-Event Distribution Learning"]
  H --> K["New Paradigm for<br>Event Stream Prediction<br>Beyond Stochastic Processes"]

Cited References (39)

1. A Stochastic Model for Order Book Dynamics (2010)
2. Long-Time Behavior of a Hawkes Process-Based Limit Order Book (2015)
3. The Neural Hawkes Process: A Neurally Self-Modulating Multivariate Point Process (2017)
4. Self-Attentive Hawkes Process (2020)
5. Deep Reinforcement Learning for Market Making Under a Hawkes Process-Based Limit Order Book Model (2022)
6. State Dependent Parallel Neural Hawkes Process for Limit Order Book Event Stream Prediction and Simulation (2022)
7. Neural Marked Hawkes Process for Limit Order Book Modeling (2024)
8. Deep Unsupervised Learning using Nonequilibrium Thermodynamics (2015)

1 of 39 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.