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.

Keywords: Queue-Reactive Model, Limit Order Books (LOB), Hidden Brownian Efficient Price, Maximum Likelihood Estimation, Market Microstructure, Equities

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 5.0/10
  • Quadrant: Holy Grail
  • Why: The paper presents a complex Markovian framework with advanced stochastic calculus, proofs of stability, and a PDE-based likelihood approximation, indicating high mathematical density. Empirically, it includes a numerical testing procedure, a real-data application, and a backtest for liquidation strategies, giving it substantial practical validation.
  flowchart TD
    A["Research Goal<br>Unify Queue-Reactive &<br>Signal-Driven LOB Models"] --> B["Model Formulation<br>Hidden Brownian Efficient Price<br>Multi-dimensional Dynamics"]
    B --> C["Theoretical Analysis<br>Prove Mid-Price Stability &<br>Macroscopic Diffusive Behavior"]
    B --> D["Estimation & Testing<br>Maximum Likelihood Estimation<br>Numerical Validation"]
    C & D --> E["Application<br>Backtesting Trading Strategies<br>in Liquidation Context"]
    E --> F["Key Outcomes<br>Unified Framework<br>Cross-Asset Correlation<br>Validated Methodology"]