Market Impact in a Latent Order Book

TL;DR

This paper extends a latent order book model by incorporating mean-reversion in agents, leading to new dynamics and insights into price impact, supported by theoretical analysis and extensive numerical simulations.

Contribution

It introduces mean-reversion into the latent order book model, resulting in novel order book dynamics and a flexible framework for better data calibration.

Findings

New order book dynamics with mean-reversion behavior

Development of a simulation scheme for the entire order book

Analysis of price impact in the extended model

Abstract

The latent order book of \cite{donier2015fully} is one of the most promising agent-based models for market impact. This work extends the minimal model by allowing agents to exhibit mean-reversion, a commonly observed pattern in real markets. This modification leads to new order book dynamics, which we explicitly study and analyze. Underlying our analysis is a mean-field assumption that views the order book through its \textit{average} density. We show how price impact develops in this new model, providing a flexible family of solutions that can potentially improve calibration to real data. While no closed-form solution is provided, we complement our theoretical investigation with extensive numerical results, including a simulation scheme for the entire order book.