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Market impact in a latent order book

Ismael Lemhadri
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Ismael Lemhadri: CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique

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Abstract: We revisit the classical problem of market impact through the lens of a new agent-based model. Drawing from the mean-field approach in Statistical Mechanics and Physics, we assume a large number of 'agents' interacting in the order book. By taking the 'continuum' limit we obtain a set of nonlinear differential equations, the core of our dynamical theory of price formation. And we explicitly solve them using Fourier analysis. One could talk as well of a "micro-macro" approach of equilibrium, where the market price is the consequence of each ("microscopic") agent behaving with respect to his preferences and to global ("macroscopic") information. When a large market order (or "metaorder") perturbs the market, our model recovers the square-root law of impact, providing new insights on the price formation process. In addition, we give various limiting cases, examples and possible extensions.

Keywords: mean-eld games; market microstructure; optimal execution strategies; reaction- diusion; agent-based models; latent order book; price formation; market impact (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-hme and nep-mst
Date: 2018-02-21
Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-01711192v2
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