Deep Learning Meets Queue-Reactive: A Framework for Realistic Limit Order Book Simulation

TL;DR

This paper introduces the MDQR model, an advanced limit order book simulation framework that combines deep learning with queue-reactive modeling to better capture market dynamics and properties.

Contribution

The MDQR model extends the Queue-Reactive framework by relaxing queue independence, adding market features, and modeling order sizes using neural networks.

Findings

Captures the square-root law of market impact

Models cross-queue correlations accurately

Reproduces realistic order size distributions

Abstract

The Queue-Reactive model introduced by Huang et al. (2015) has become a standard tool for limit order book modeling, widely adopted by both researchers and practitioners for its simplicity and effectiveness. We present the Multidimensional Deep Queue-Reactive (MDQR) model, which extends this framework in three ways: it relaxes the assumption of queue independence, enriches the state space with market features, and models the distribution of order sizes. Through a neural network architecture, the model learns complex dependencies between different price levels and adapts to varying market conditions, while preserving the interpretable point-process foundation of the original framework. Using data from the Bund futures market, we show that MDQR captures key market properties including the square-root law of market impact, cross-queue correlations, and realistic order size patterns. The model demonstrates particular strength in reproducing both conditional and stationary distributions of order sizes, as well as various stylized facts of market microstructure. The model achieves this while maintaining the computational efficiency needed for practical applications such as strategy development through reinforcement learning or realistic backtesting.