Mean-Reverting Agents in Latent Order Book Impact Models

Summary

This work extends a latent order book model of market impact by allowing agents to exhibit mean-reverting behavior, a pattern commonly observed in markets. It studies the resulting order book dynamics using a mean-field assumption, which represents the book through its average density. The analysis examines how price impact develops and derives a flexible family of solutions intended to support calibration to market data.

The paper provides theoretical analysis and numerical results, including a simulation scheme for the full order book. It does not provide a closed-form solution, and the excerpt does not specify empirical calibration results or show that the model improves trading performance. Its contribution is a modeling extension and a way to explore impact dynamics, with practical value dependent on calibration against real market observations.

Key ideas

• The model extends a latent order book framework by adding mean-reverting agent behavior.
• A mean-field assumption describes the order book through its average density.
• The analysis studies how price impact emerges under the modified dynamics.
• A flexible family of solutions may support calibration to observed data.
• The work supplies numerical results and a full order book simulation scheme but no closed-form solution.

Tags

# Market Impact in a Latent Order Book


# Market Impact in a Latent Order Book









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.

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