A Fully Consistent, Minimal Model for Non-Linear Market Impact

17 Pages Posted: 30 Nov 2014 Last revised: 2 Dec 2014

See all articles by Jonathan Donier

Jonathan Donier

Université Paris VI Pierre et Marie Curie

Julius Bonart

Capital Fund Management

Iacopo Mastromatteo

Capital Fund Management

Jean-Philippe Bouchaud

Capital Fund Management

Date Written: December 1, 2014

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.

Keywords: market microstructure, price formation, market impact, reaction-diffusion, limit order book, non-arbitrage

Suggested Citation

Donier, Jonathan and Bonart, Julius and Mastromatteo, Iacopo and Bouchaud, Jean-Philippe, A Fully Consistent, Minimal Model for Non-Linear Market Impact (December 1, 2014). Available at SSRN: https://ssrn.com/abstract=2531917 or http://dx.doi.org/10.2139/ssrn.2531917

Jonathan Donier (Contact Author)

Université Paris VI Pierre et Marie Curie ( email )

175 Rue du Chevaleret
Paris, 75013
France

Julius Bonart

Capital Fund Management ( email )

23 rue de l'Université
Paris, 75007
France

Iacopo Mastromatteo

Capital Fund Management ( email )

France

Jean-Philippe Bouchaud

Capital Fund Management ( email )

23 rue de l'Université
Paris, 75007
France
+33 1 49 49 59 20 (Phone)

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