Market Impact in a Latent Order Book

I. Lemhadri

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

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.

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