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A simple microstructural explanation of the concavity of price impact

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  • Sergey Nadtochiy

Abstract

This article provides a simple explanation of the asymptotic concavity of the price impact of a meta-order via the microstructural properties of the market. This explanation is made more precise by a model in which the local relationship between the order flow and the fundamental price (i.e. the local price impact) is linear, with a constant slope, which makes the model dynamically consistent. Nevertheless, the expected impact on midprice from a large sequence of co-directional trades is nonlinear and asymptotically concave. The main practical conclusion of the proposed explanation is that, throughout a meta-order, the volumes at the best bid and ask prices change (on average) in favor of the executor. This conclusion, in turn, relies on two more concrete predictions, one of which can be tested, at least for large-tick stocks, using publicly available market data.

Suggested Citation

  • Sergey Nadtochiy, 2020. "A simple microstructural explanation of the concavity of price impact," Papers 2001.01860, arXiv.org, revised Dec 2020.
    • Handle: RePEc:arx:papers:2001.01860
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    References listed on IDEAS

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    1. 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.
    2. Nataliya Bershova & Dmitry Rakhlin, 2013. "The non-linear market impact of large trades: evidence from buy-side order flow," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1759-1778, November.
    3. Mathias Pohl & Alexander Ristig & Walter Schachermayer & Ludovic Tangpi, 2017. "The amazing power of dimensional analysis: Quantifying market impact," Papers 1702.05434, arXiv.org, revised Sep 2017.
    4. Sasha Stoikov, 2018. "The micro-price: a high-frequency estimator of future prices," Quantitative Finance, Taylor & Francis Journals, vol. 18(12), pages 1959-1966, December.
    5. Roman Gayduk & Sergey Nadtochiy, 2018. "Liquidity effects of trading frequency," Mathematical Finance, Wiley Blackwell, vol. 28(3), pages 839-876, July.
    6. Roman Gayduk & Sergey Nadtochiy, 2017. "Control-stopping Games for Market Microstructure and Beyond," Papers 1708.00506, arXiv.org, revised Mar 2019.
    7. J. Doyne Farmer & Austin Gerig & Fabrizio Lillo & Henri Waelbroeck, 2013. "How efficiency shapes market impact," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1743-1758, November.
    8. Bence Toth & Yves Lemperiere & Cyril Deremble & Joachim de Lataillade & Julien Kockelkoren & Jean-Philippe Bouchaud, 2011. "Anomalous price impact and the critical nature of liquidity in financial markets," Papers 1105.1694, arXiv.org, revised Nov 2011.
    9. Fédéric Bucci & Michael Benzaquen & Fabrizio Lillo & Jean-Philippe Bouchaud, 2019. "Crossover from Linear to Square-Root Market Impact," Post-Print hal-02323405, HAL.
    10. J. Donier & J. Bonart & I. Mastromatteo & J.-P. Bouchaud, 2015. "A fully consistent, minimal model for non-linear market impact," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1109-1121, July.
    11. Jonathan Donier & Julius Bonart & Iacopo Mastromatteo & Jean-Philippe Bouchaud, 2014. "A fully consistent, minimal model for non-linear market impact," Papers 1412.0141, arXiv.org, revised Mar 2015.
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    Cited by:

    1. Yan Dolinsky & Shir Moshe, 2021. "Utility Indifference Pricing with High Risk Aversion and Small Linear Price Impact," Papers 2111.00451, arXiv.org, revised Jan 2022.

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