Agent-Based Models Explain Robust Square-Root Market Impact

Summary

This paper revisits an agent-based model designed to explain why the price impact of large meta-orders grows approximately with the square root of traded volume. The model assumes that much market liquidity is latent and decreases near the current price as prices diffuse. The authors examine criticisms of the original setup, in which market orders carry the informed behavior while limit orders arrive passively and randomly. They explore variants where limit orders respond to order flow and where execution protocols change.

Across these alternatives, the square-root impact relationship remains robust, suggesting it can arise from relatively few market ingredients. The study also reinterprets an earlier reported switch from super-diffusive to sub-diffusive price behavior as a crossover rather than a true phase transition. A modest change to the model can produce a genuine transition. Finally, the authors outline a theoretical account of how nonlinear impact can persist even when order-flow bias becomes very small. These are model-based findings; the abstract provides no empirical market validation or quantitative performance estimates.

Key ideas

• The model links square-root meta-order impact to latent liquidity that thins near the current price.
• The authors test changes to limit-order behavior and execution protocols.
• The square-root impact law persists across the model variants studied.
• The reported change from super-diffusion to sub-diffusion is characterized as a crossover in the original model.
• A modified model can produce a genuine phase transition and nonlinear impact under very small order-flow bias.

Tags

# Agent-based models for latent liquidity and concave price impact


# Agent-based models for latent liquidity and concave price impact









We revisit the "epsilon-intelligence" model of Toth et al.(2011), that was proposed as a minimal framework to understand the square-root dependence of the impact of meta-orders on volume in financial markets. The basic idea is that most of the daily liquidity is "latent" and furthermore vanishes linearly around the current price, as a consequence of the diffusion of the price itself. However, the numerical implementation of Toth et al. was criticised as being unrealistic, in particular because all the "intelligence" was conferred to market orders, while limit orders were passive and random. In this work, we study various alternative specifications of the model, for example allowing limit orders to react to the order flow, or changing the execution protocols. By and large, our study lends strong support to the idea that the square-root impact law is a very generic and robust property that requires very few ingredients to be valid. We also show that the transition from super-diffusion to sub-diffusion reported in Toth et al. is in fact a cross-over, but that the original model can be slightly altered in order to give rise to a genuine phase transition, which is of interest on its own. We finally propose a general theoretical framework to understand how a non-linear impact may appear even in the limit where the bias in the order flow is vanishingly small.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.