Work

The two square root laws of market impact and the role of sophisticated market participants

Year: 2026

Type: article

Abstract: The goal of this paper is to disentangle the roles of volume and of participation rate in the price response of the market to a sequence of transactions. To do so, we are inspired the methodology introduced in (Quant. Finance 15 (2015) 1123–1135; Math. Finance 30 (2020) 1309–1336) where price dynamics are derived from order flow dynamics using no arbitrage assumptions. We extend this approach by taking into account a sophisticated market participant having superior abilities to analyse market dynamics. Our results lead to the recovery of two square root laws: (i) For a given participation rate, during the execution of a metaorder, the market impact evolves in a square root manner with respect to the cumulated traded volume. (ii) For a given executed volume Q, the market impact is proportional to γ, where γ denotes the participation rate, for γ large enough. Smaller participation rates induce a more linear dependence of the market impact in the participation rate.

Source: The Annals of Applied Probability

DOI: 10.1214/26-aap2311

Authors: Bruno Durin, Mathieu Rosenbaum, Grégoire Szymanski

Institutions: Centre de Recherche en Mathématiques de la Décision, Université Paris Dauphine-PSL, University of Luxembourg

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

OpenAlex ID: W4389260932

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