IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2001.01860.html
   My bibliography  Save this paper

A simple microstructural explanation of the concavity of price impact

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2001.01860
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sergey Nadtochiy, 2022. "A simple microstructural explanation of the concavity of price impact," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 78-113, January.
    2. Emilio Said, 2022. "Market Impact: Empirical Evidence, Theory and Practice," Working Papers hal-03668669, HAL.
    3. Fabrizio Lillo, 2021. "Order flow and price formation," Papers 2105.00521, arXiv.org.
    4. Emilio Said, 2022. "Market Impact: Empirical Evidence, Theory and Practice," Papers 2205.07385, arXiv.org.
    5. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    6. 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.
    7. Fr'ed'eric Bucci & Michael Benzaquen & Fabrizio Lillo & Jean-Philippe Bouchaud, 2019. "Slow decay of impact in equity markets: insights from the ANcerno database," Papers 1901.05332, arXiv.org, revised Jan 2019.
    8. Fr'ed'eric Bucci & Iacopo Mastromatteo & Michael Benzaquen & Jean-Philippe Bouchaud, 2019. "Impact is not just volatility," Papers 1905.04569, arXiv.org.
    9. Thibault Jaisson, 2014. "Market impact as anticipation of the order flow imbalance," Papers 1402.1288, arXiv.org.
    10. Louis Saddier & Matteo Marsili, 2023. "A Bayesian theory of market impact," Papers 2303.08867, arXiv.org, revised May 2024.
    11. Frédéric Bucci & Michael Benzaquen & Fabrizio Lillo & Jean-Philippe Bouchaud, 2019. "Slow Decay of Impact in Equity Markets: Insights from the ANcerno Database," Post-Print hal-02323357, HAL.
    12. Frédéric Bucci & Iacopo Mastromatteo & Michael Benzaquen & Jean-Philippe Bouchaud, 2019. "Impact is not just volatility," Post-Print hal-02323182, HAL.
    13. Jonathan Donier & Julius Bonart, 2014. "A Million Metaorder Analysis of Market Impact on the Bitcoin," Papers 1412.4503, arXiv.org, revised Sep 2015.
    14. Jean-Philippe Bouchaud, 2021. "The Inelastic Market Hypothesis: A Microstructural Interpretation," Papers 2108.00242, arXiv.org, revised Jan 2022.
    15. Brunovský, Pavol & Černý, Aleš & Komadel, Ján, 2018. "Optimal trade execution under endogenous pressure to liquidate: Theory and numerical solutions," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1159-1171.
    16. Elia Zarinelli & Michele Treccani & J. Doyne Farmer & Fabrizio Lillo, 2014. "Beyond the square root: Evidence for logarithmic dependence of market impact on size and participation rate," Papers 1412.2152, arXiv.org.
    17. Emilio Said & Ahmed Bel Hadj Ayed & Damien Thillou & Jean-Jacques Rabeyrin & Frédéric Abergel, 2020. "Market Impact: A Systematic Study of the High Frequency Options Market," Post-Print hal-02014248, HAL.
    18. Jonathan Donier & Jean-Philippe Bouchaud, 2015. "Why Do Markets Crash? Bitcoin Data Offers Unprecedented Insights," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-11, October.
    19. Jonathan Donier & Jean-Philippe Bouchaud, 2015. "Why Do Markets Crash? Bitcoin Data Offers Unprecedented Insights," Post-Print hal-01277584, HAL.
    20. Francesco Cordoni & Fabrizio Lillo, 2022. "Transient impact from the Nash equilibrium of a permanent market impact game," Papers 2205.00494, arXiv.org, revised Mar 2023.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2001.01860. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.