%0 Journal Article
%T A fully consistent, minimal model for non-linear market impact
%A Jonathan Donier
%A Julius Bonart
%A Iacopo Mastromatteo
%A Jean-Philippe Bouchaud
%J Quantitative Finance
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1412.0141v4