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Market impact in a latent order book

Author

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  • Ismael Lemhadri

    (CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Ismael Lemhadri, 2018. "Market impact in a latent order book," Working Papers hal-01711192, HAL.
    • Handle: RePEc:hal:wpaper:hal-01711192
    Note: View the original document on HAL open archive server: https://hal.science/hal-01711192v2
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    References listed on IDEAS

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    Cited by:

    1. Guillermo Angeris & Alex Evans & Tarun Chitra, 2020. "When does the tail wag the dog? Curvature and market making," Papers 2012.08040, arXiv.org.
    2. Mariani, Francesca & Recchioni, Maria Cristina & Ciommi, Mariateresa, 2019. "Merton’s portfolio problem including market frictions: A closed-form formula supporting the shadow price approach," European Journal of Operational Research, Elsevier, vol. 275(3), pages 1178-1189.

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    More about this item

    Keywords

    mean-eld games; market microstructure; optimal execution strategies; reaction- diusion; agent-based models; latent order book; price formation; market impact;
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