A fully consistent, minimal model for non-linear market impact

TL;DR

This paper introduces a minimal, consistent model for non-linear market impact based on a linear order book, explaining the square-root impact law and providing insights into price trajectories, manipulation, and impact components.

Contribution

It presents a novel minimal theoretical framework that generalizes existing models, accounting for non-linear impact, price manipulation prevention, and impact decomposition.

Findings

Reproduces the universal square-root impact law.

Predicts non-trivial price trajectories during trading interruptions or reversals.

Ensures the model is free of price manipulation and prices can be diffusive.

Abstract

We propose a minimal theory of non-linear price impact based on a linear (latent) order book approximation, inspired by diffusion-reaction models and general arguments. Our framework allows one to compute the average price trajectory in the presence of a meta-order, that consistently generalizes previously proposed propagator models. We account for the universally observed square-root impact law, and predict non-trivial trajectories when trading is interrupted or reversed. We prove that our framework is free of price manipulation, and that prices can be made diffusive (albeit with a generic short-term mean-reverting contribution). Our model suggests that prices can be decomposed into a transient "mechanical" impact component and a permanent "informational" component.