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

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  • Jonathan Donier
  • Julius Bonart
  • Iacopo Mastromatteo
  • Jean-Philippe Bouchaud

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.

Suggested Citation

  • Jonathan Donier & Julius Bonart & Iacopo Mastromatteo & Jean-Philippe Bouchaud, 2014. "A fully consistent, minimal model for non-linear market impact," Papers 1412.0141, arXiv.org, revised Mar 2015.
    • Handle: RePEc:arx:papers:1412.0141
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    File URL: http://arxiv.org/pdf/1412.0141
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