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

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  • Bruno Durin
  • Mathieu Rosenbaum
  • Gr'egoire Szymanski

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 arXiv:1402.1288, arXiv:1805.07134 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 $\sqrt{\gamma}$, where $\gamma$ denotes the participation rate, for $\gamma$ large enough. Smaller participation rates induce a more linear dependence of the market impact in the participation rate.

Suggested Citation

  • Bruno Durin & Mathieu Rosenbaum & Gr'egoire Szymanski, 2023. "The two square root laws of market impact and the role of sophisticated market participants," Papers 2311.18283, arXiv.org.
    • Handle: RePEc:arx:papers:2311.18283
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    References listed on IDEAS

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    9. Omar El Euch & Mathieu Rosenbaum, 2019. "The characteristic function of rough Heston models," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 3-38, January.
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    Cited by:

    1. Youssef Ouazzani Chahdi & Mathieu Rosenbaum & Gr'egoire Szymanski, 2024. "A theory of passive market impact," Papers 2412.07461, arXiv.org.
    2. Eduardo Abi Jaber & Alessandro Bondi & Nathan De Carvalho & Eyal Neuman & Sturmius Tuschmann, 2025. "Fredholm Approach to Nonlinear Propagator Models," Papers 2503.04323, arXiv.org.
    3. Paolo Dai Pra & Paolo Pigato, 2025. "A Stochastic Volatility Approximation for a Tick-By-Tick Price Model with Mean-Field Interaction," CEIS Research Paper 596, Tor Vergata University, CEIS, revised 08 Apr 2025.
    4. Paolo Dai Pra & Paolo Pigato, 2025. "A stochastic volatility approximation for a tick-by-tick price model with mean-field interaction," Papers 2504.03445, arXiv.org.
    5. Gr'egoire Szymanski & Wei Xu, 2025. "Mean-Field Limits for Nearly Unstable Hawkes Processes," Papers 2501.11648, arXiv.org.

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