Market Impact in a Latent Order Book

I. Lemhadri

Market Microstructure and Liquidity, 2020

Best Internship in Applied Mathematics Award, 2017, Ecole Polytechnique.

We revisit the problem of market impact through the lens of the latent order book, first introduced by Donier, Bonart, Mastromatteo and Bouchaud. Drawing from the mean-field approach in Statistical Mechanics and Physics, this model assumes a large number of 'agents' interacting in the order book. By taking the 'continuum' limit this leads to a set of nonlinear differential equations, the core of our dynamical theory of price formation. 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 "meta-order") perturbs the market, the model recovers the square-root law of impact, providing new insights on the price formation process. We analyze this model in depth: on the theoretical front, establishing existence and uniqueness properties, and on the applied front, studying various limiting cases, examples and possible extensions.



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