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

TL;DR

The Multidimensional Deep Queue-Reactive (MDQR) model is presented, 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.

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.

Figures (21)

• Figure 1: Transition matrix of events on simulated markets vs historical data. The rows of the matrix represent the conditional probabilities of observing a specific event type given the type of the previous event (intra-sides).
• Figure 2: Comparison of DQR (with $x_k = [q_k, h_k]$) and QR trade order arrival intensities across trading hours, averaged over queue sizes.
• Figure 3: Model performance comparison across different feature sets: (1) Vanilla QR model ($x_k = q_k$), (2) $x_k = [q_k, h_k]$, (3) $x_k = [q_k, \eta_{k-1}]$, (4) $x_k = [q_k, h_k, \eta_{k-1}]$. Metrics: log-likelihood (higher is better), balanced accuracy of next-event prediction (higher is better), and relative difference in time to next event (lower is better).
• Figure 4: A conceptual illustration of the transition from a single-queue model (left) to the multidimensional MDQR framework (right). In the single-queue scenario, events occur at one level and are of three types (L, C, M). In the multidimensional scenario, multiple levels on both sides of the order book are considered together, resulting in a larger event space and enabling the model to capture cross-level interactions and dependencies.
• Figure 5: Training and validation negative log-likelihood loss evolution for the order intensity model. The main plot shows the full training trajectory, while the inset focuses on epochs 70-94 to highlight convergence behavior.