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

Jonathan Donier, Julius Bonart, Iacopo Mastromatteo and Jean-Philippe Bouchaud

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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.

Date: 2014-11, Revised 2015-03
New Economics Papers: this item is included in nep-mst
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1412.0141

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