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The Subtle Interplay between Square-root Impact, Order Imbalance & Volatility II: An Artificial Market Generator

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  • Guillaume Maitrier
  • Gr'egoire Loeper
  • Jean-Philippe Bouchaud

Abstract

This work extends and complements our previous theoretical paper on the subtle interplay between impact, order flow and volatility. In the present paper, we generate synthetic market data following the specification of that paper and show that the approximations made there are actually justified, which provides quantitative support our conclusion that price volatility can be fully explained by the superposition of correlated metaorders which all impact prices, on average, as a square-root of executed volume. One of the most striking predictions of our model is the structure of the correlation between generalized order flow and returns, which is observed empirically and reproduced using our synthetic market generator. Furthermore, we were able to construct proxy metaorders from our simulated order flow that reproduce the square-root law of market impact, lending further credence to the proposal made in Ref. [2] to measure the impact of real metaorders from tape data (i.e. anonymized trades), which was long thought to be impossible.

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  • Guillaume Maitrier & Gr'egoire Loeper & Jean-Philippe Bouchaud, 2025. "The Subtle Interplay between Square-root Impact, Order Imbalance & Volatility II: An Artificial Market Generator," Papers 2509.05065, arXiv.org.
    • Handle: RePEc:arx:papers:2509.05065
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    References listed on IDEAS

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    1. Louis Saddier & Matteo Marsili, 2023. "A Bayesian theory of market impact," Papers 2303.08867, arXiv.org, revised May 2024.
    2. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2006. "Institutional Investors and Stock Market Volatility," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(2), pages 461-504.
    3. Guillaume Maitrier & Jean-Philippe Bouchaud, 2025. "The Subtle Interplay between Square-root Impact, Order Imbalance & Volatility: A Unifying Framework," Papers 2506.07711, arXiv.org, revised Jul 2025.
    4. Hasbrouck, Joel, 2007. "Empirical Market Microstructure: The Institutions, Economics, and Econometrics of Securities Trading," OUP Catalogue, Oxford University Press, number 9780195301649.
    5. Guillaume Maitrier & Gr'egoire Loeper & Jean-Philippe Bouchaud, 2025. "Generating realistic metaorders from public data," Papers 2503.18199, arXiv.org, revised Apr 2025.
    6. Jean-Philippe Bouchaud & Marc Mezard, 1997. "Universality classes for extreme value statistics," Science & Finance (CFM) working paper archive 500043, Science & Finance, Capital Fund Management.
    7. Damian Eduardo Taranto & Giacomo Bormetti & Jean-Philippe Bouchaud & Fabrizio Lillo & Bence Tóth, 2018. "Linear models for the impact of order flow on prices. I. History dependent impact models," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 903-915, June.
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    Cited by:

    1. Axel Ciceri & Austin Cottrell & Joshua Freeland & Daniel Fry & Hirotoshi Hirai & Philip Intallura & Hwajung Kang & Chee-Kong Lee & Abhijit Mitra & Kentaro Ohno & Das Pemmaraju & Manuel Proissl & Brian, 2025. "Enhanced fill probability estimates in institutional algorithmic bond trading using statistical learning algorithms with quantum computers," Papers 2509.17715, arXiv.org.

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