Multi-dimensional queue-reactive model and signal-driven models: a unified framework

TL;DR

This paper introduces a unified Markovian framework combining queue-reactive and signal-driven models to better understand and predict limit order book dynamics and price behavior, with applications in trading strategy backtesting.

Contribution

It extends queue-reactive models to incorporate efficient prices and signals, providing a comprehensive framework for multi-stock order book analysis.

Findings

Prices behave as diffusions at the macroscopic scale.

The model's maximum likelihood estimation is effective.

Backtested trading strategies show practical utility.

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.