Price Impact in a Latent Order Book

The latent order book of [Donier et al., 2015, A fully consistent, minimal model for nonlinear market impact, Quantitative Finance 15(7), 1109-1121] 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 average density. We show how price impact develops in this new model, providing a flexible family of solutions that can potentially be calibrated 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.