Autoregressive Deep State-Space Models for Limit Order Book Message Flow

Summary

This paper develops an autoregressive model that generates tokenized limit order book messages, which a simulator uses to update the book state. Its architecture uses simplified structured state-space layers to process long sequences of messages and states. The authors also create a tokenizer for NASDAQ order messages in LOBSTER data, grouping successive digits into tokens.

In out-of-sample evaluation, the model approximates the observed message distribution with low perplexity. Mid-price returns computed from its generated order flow are significantly correlated with the data, which the paper presents as evidence of conditional forecasting ability. The authors suggest that detailed synthetic order flow could support work beyond forecasting, including as a simulated environment for high-frequency reinforcement learning. These results concern the reported dataset and measures; the abstract does not provide broader market validation, execution results, or evidence that simulated flows reproduce every feature needed for trading applications.

Key ideas

• The model generates sequences of tokenized limit order book messages autoregressively.
• Structured state-space layers are used to process long message and book-state sequences.
• A custom tokenizer is applied to NASDAQ equity order messages from LOBSTER data.
• Out-of-sample evaluation reports low perplexity and significant correlation between generated and observed mid-price returns.
• Synthetic order flow may serve as a modeling environment for high-frequency research, though broader validation is not described.

Tags

# 2309.00638


# Generative AI for End-to-End Limit Order Book Modelling: A Token-Level Autoregressive Generative Model of Message Flow Using a Deep State Space Network









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.