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Developing a generative model of realistic order flow in financial markets isa challenging open problem, with numerous applications for market participants.Addressing this, we propose the first end-to-end autoregressive generativemodel that generates tokenized limit order book (LOB) messages. These messagesare interpreted by a Jax-LOB simulator, which updates the LOB state. To handlelong sequences efficiently, the model employs simplified structured state-spacelayers to process sequences of order book states and tokenized messages. UsingLOBSTER data of NASDAQ equity LOBs, we develop a custom tokenizer for messagedata, converting groups of successive digits to tokens, similar to tokenizationin large language models. Out-of-sample results show promising performance inapproximating the data distribution, as evidenced by low model perplexity.Furthermore, the mid-price returns calculated from the generated order flowexhibit a significant correlation with the data, indicating impressiveconditional forecast performance. Due to the granularity of generated data, andthe accuracy of the model, it offers new application areas for future workbeyond forecasting, e.g. acting as a world model in high-frequency financialreinforcement learning applications. Overall, our results invite the use andextension of the model in the direction of autoregressive large financialmodels for the generation of high-frequency financial data and we commit toopen-sourcing our code to facilitate future research.

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