A Fully Consistent, Minimal Model for Non-Linear Market Impact
17 Pages Posted: 30 Nov 2014 Last revised: 2 Dec 2014
Date Written: December 1, 2014
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.
Keywords: market microstructure, price formation, market impact, reaction-diffusion, limit order book, non-arbitrage
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