Queue-Reactive Model

Reinforcement Learning in Queue-Reactive Models: Application to Optimal Execution ArXiv ID: 2511.15262 “View on arXiv” Authors: Tomas Espana, Yadh Hafsi, Fabrizio Lillo, Edoardo Vittori Abstract We investigate the use of Reinforcement Learning for the optimal execution of meta-orders, where the objective is to execute incrementally large orders while minimizing implementation shortfall and market impact over an extended period of time. Departing from traditional parametric approaches to price dynamics and impact modeling, we adopt a model-free, data-driven framework. Since policy optimization requires counterfactual feedback that historical data cannot provide, we employ the Queue-Reactive Model to generate realistic and tractable limit order book simulations that encompass transient price impact, and nonlinear and dynamic order flow responses. Methodologically, we train a Double Deep Q-Network agent on a state space comprising time, inventory, price, and depth variables, and evaluate its performance against established benchmarks. Numerical simulation results show that the agent learns a policy that is both strategic and tactical, adapting effectively to order book conditions and outperforming standard approaches across multiple training configurations. These findings provide strong evidence that model-free Reinforcement Learning can yield adaptive and robust solutions to the optimal execution problem. ...

Multi-dimensional queue-reactive model and signal-driven models: a unified framework ArXiv ID: 2506.11843 “View on arXiv” Authors: Emmanouil Sfendourakis Abstract We present a Markovian market model driven by a hidden Brownian efficient price. In particular, we extend the queue-reactive model, making its dynamics dependent on the efficient price. Our study focuses on two sub-models: a signal-driven price model where the mid-price jump rates depend on the efficient price and an observable signal, and the usual queue-reactive model dependent on the efficient price via the intensities of the order arrivals. This way, we are able to correlate the evolution of limit order books of different stocks. We prove the stability of the observed mid-price around the efficient price under natural assumptions. Precisely, we show that at the macroscopic scale, prices behave as diffusions. We also develop a maximum likelihood estimation procedure for the model, and test it numerically. Our model is them used to backest trading strategies in a liquidation context. ...

Deep Learning Meets Queue-Reactive: A Framework for Realistic Limit Order Book Simulation ArXiv ID: 2501.08822 “View on arXiv” Authors: Unknown 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. ...

A Novel Approach to Queue-Reactive Models: The Importance of Order Sizes ArXiv ID: 2405.18594 “View on arXiv” Authors: Unknown Abstract In this article, we delve into the applications and extensions of the queue-reactive model for the simulation of limit order books. Our approach emphasizes the importance of order sizes, in conjunction with their type and arrival rate, by integrating the current state of the order book to determine, not only the intensity of order arrivals and their type, but also their sizes. These extensions generate simulated markets that are in line with numerous stylized facts of the market. Our empirical calibration, using futures on German bonds, reveals that the extended queue-reactive model significantly improves the description of order flow properties and the shape of queue distributions. Moreover, our findings demonstrate that the extended model produces simulated markets with a volatility comparable to historical real data, utilizing only endogenous information from the limit order book. This research underscores the potential of the queue-reactive model and its extensions in accurately simulating market dynamics and providing valuable insights into the complex nature of limit order book modeling. ...