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Crossover from Linear to Square-Root Market Impact

Author

Listed:
  • Fédéric Bucci
  • Michael Benzaquen

    (LadHyX - Laboratoire d'hydrodynamique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Fabrizio Lillo
  • Jean-Philippe Bouchaud

Abstract

Using a large database of 8 million institutional trades executed in the U.S. equity market, we establish a clear crossover between a linear market impact regime and a square-root regime as a function of the volume of the order. Our empirical results are remarkably well explained by a recently proposed dynamical theory of liquidity that makes specific predictions about the scaling function describing this crossover. Allowing at least two characteristic timescales for the liquidity ("fast" and "slow") enables one to reach quantitative agreement with the data.

Suggested Citation

  • Fédéric Bucci & Michael Benzaquen & Fabrizio Lillo & Jean-Philippe Bouchaud, 2019. "Crossover from Linear to Square-Root Market Impact," Post-Print hal-02323405, HAL.
    • Handle: RePEc:hal:journl:hal-02323405
    DOI: 10.1103/PhysRevLett.122.108302
    Note: View the original document on HAL open archive server: https://hal.science/hal-02323405
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    Citations

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    Cited by:

    1. Mohammed Salek & Damien Challet & Ioane Muni Toke, 2023. "Price impact in equity auctions: zero, then linear," Working Papers hal-03938660, HAL.
    2. Fr'ed'eric Bucci & Iacopo Mastromatteo & Michael Benzaquen & Jean-Philippe Bouchaud, 2019. "Impact is not just volatility," Papers 1905.04569, arXiv.org.
    3. David Marcos, 2020. "Transaction Costs in Execution Trading," Papers 2007.07998, arXiv.org.
    4. Shota Imaki & Kentaro Imajo & Katsuya Ito & Kentaro Minami & Kei Nakagawa, 2021. "No-Transaction Band Network: A Neural Network Architecture for Efficient Deep Hedging," Papers 2103.01775, arXiv.org.
    5. Stanis{l}aw Dro.zd.z & Jaros{l}aw Kwapie'n & Marcin Wk{a}torek, 2023. "What is mature and what is still emerging in the cryptocurrency market?," Papers 2305.05751, arXiv.org.
    6. Fabrizio Lillo, 2021. "Order flow and price formation," Papers 2105.00521, arXiv.org.
    7. Sergey Nadtochiy, 2020. "A simple microstructural explanation of the concavity of price impact," Papers 2001.01860, arXiv.org, revised Dec 2020.
    8. Roncalli, Thierry & Cherief, Amina & Karray-Meziou, Fatma & Regnault, Margaux, 2021. "Liquidity Stress Testing in Asset Management - Part 2. Modeling the Asset Liquidity Risk," MPRA Paper 108295, University Library of Munich, Germany.
    9. Louis Saddier & Matteo Marsili, 2023. "A Bayesian theory of market impact," Papers 2303.08867, arXiv.org, revised May 2024.
    10. Lukas Gonon & Johannes Muhle‐Karbe & Xiaofei Shi, 2021. "Asset pricing with general transaction costs: Theory and numerics," Mathematical Finance, Wiley Blackwell, vol. 31(2), pages 595-648, April.
    11. Frédéric Bucci & Iacopo Mastromatteo & Michael Benzaquen & Jean-Philippe Bouchaud, 2019. "Impact is not just volatility," Post-Print hal-02323182, HAL.
    12. Sergey Nadtochiy, 2022. "A simple microstructural explanation of the concavity of price impact," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 78-113, January.
    13. Rodriguez, E. & Alvarez-Ramirez, J., 2021. "Time-varying cross-correlation between trading volume and returns in US stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).

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