Paper: arXiv 2309.00638

Abstract

Developing a generative model of realistic order flow in financial markets is a challenging open problem, with numerous applications for market participants. Addressing this, we propose the first end-to-end autoregressive generative model that generates tokenized limit order book (LOB) messages. These messages are interpreted by a Jax-LOB simulator, which updates the LOB state. To handle long sequences efficiently, the model employs simplified structured state-space layers to process sequences of order book states and tokenized messages. Using LOBSTER data of NASDAQ equity LOBs, we develop a custom tokenizer for message data, converting groups of successive digits to tokens, similar to tokenization in large language models. Out-of-sample results show promising performance in approximating the data distribution, as evidenced by low model perplexity. Furthermore, the mid-price returns calculated from the generated order flow exhibit a significant correlation with the data, indicating impressive conditional forecast performance. Due to the granularity of generated data, and the accuracy of the model, it offers new application areas for future work beyond forecasting, e.g. acting as a world model in high-frequency financial reinforcement learning applications. Overall, our results invite the use and extension of the model in the direction of autoregressive large financial models for the generation of high-frequency financial data and we commit to open-sourcing our code to facilitate future research.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced state-space models (S5) and detailed statistical metrics (perplexity, correlation), while also using real LOBSTER data and a custom Jax simulator for backtesting.

Research Flowchart

  flowchart TD
  A["Research Goal<br/>Generative model for realistic<br/>limit order book (LOB) message flow"] --> B["Methodology<br/>Token-level autoregressive generative model<br/>with structured state-space network"]
  B --> C["Data & Inputs<br/>NASDAQ LOBSTER data"]
  C --> D["Computation<br/>Custom tokenizer &<br/>Jax-LOB simulator"]
  D --> E["Findings & Outcomes<br/>Low perplexity & high correlation<br/>for mid-price returns"]
  E --> F["Implications<br/>Foundation for large<br/>financial world models"]