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Anomalous price impact and the critical nature of liquidity in financial markets


  • Bence Toth
  • Yves Lemperiere
  • Cyril Deremble
  • Joachim de Lataillade
  • Julien Kockelkoren
  • Jean-Philippe Bouchaud


We propose a dynamical theory of market liquidity that predicts that the average supply/demand profile is V-shaped and {\it vanishes} around the current price. This result is generic, and only relies on mild assumptions about the order flow and on the fact that prices are (to a first approximation) diffusive. This naturally accounts for two striking stylized facts: first, large metaorders have to be fragmented in order to be digested by the liquidity funnel, leading to long-memory in the sign of the order flow. Second, the anomalously small local liquidity induces a breakdown of linear response and a diverging impact of small orders, explaining the "square-root" impact law, for which we provide additional empirical support. Finally, we test our arguments quantitatively using a numerical model of order flow based on the same minimal ingredients.

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  • 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,, revised Nov 2011.
  • Handle: RePEc:arx:papers:1105.1694

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    References listed on IDEAS

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    8. Esteban Moro & Javier Vicente & Luis G. Moyano & Austin Gerig & J. Doyne Farmer & Gabriella Vaglica & Fabrizio Lillo & Rosario N. Mantegna, 2009. "Market impact and trading profile of large trading orders in stock markets," Papers 0908.0202,
    9. Jean-Philippe Bouchaud & J. Doyne Farmer & Fabrizio Lillo, 2008. "How markets slowly digest changes in supply and demand," Papers 0809.0822,
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    Cited by:

    1. Paolo Barucca & Fabrizio Lillo, 2017. "Behind the price: on the role of agent's reflexivity in financial market microstructure," Papers 1708.07047,
    2. Yann Braouezec & Lakshithe Wagalath, 2016. "Risk-based capital requirements and optimal liquidation in a stress scenario," Working Papers 2016-ACF-01, IESEG School of Management.
    3. Ludovic Moreau & Johannes Muhle-Karbe & H. Mete Soner, 2014. "Trading with Small Price Impact," Papers 1402.5304,, revised Mar 2015.
    4. repec:wsi:ijtafx:v:20:y:2017:i:01:n:s0219024917500017 is not listed on IDEAS
    5. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2013. "Limit order books," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1709-1742, November.
    6. Jonathan Donier & Jean-Philippe Bouchaud, 2015. "Why Do Markets Crash? Bitcoin Data Offers Unprecedented Insights," Papers 1503.06704,, revised Oct 2015.
    7. Luo, Jiawen & Chen, Langnan & Liu, Hao, 2013. "Distribution characteristics of stock market liquidity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 6004-6014.
    8. 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,
    9. Bence Toth & Imon Palit & Fabrizio Lillo & J. Doyne Farmer, 2011. "Why is order flow so persistent?," Papers 1108.1632,, revised Nov 2014.
    10. Friedrich Hubalek & Paul Kruhner & Thorsten Rheinlander, 2017. "Brownian trading excursions and avalanches," Papers 1701.00993,
    11. Radu T. Pruna & Maria Polukarov & Nicholas R. Jennings, 2016. "A new structural stochastic volatility model of asset pricing and its stylized facts," Papers 1604.08824,
    12. Damian Eduardo Taranto & Giacomo Bormetti & Jean-Philippe Bouchaud & Fabrizio Lillo & Bence Toth, 2016. "Linear models for the impact of order flow on prices II. The Mixture Transition Distribution model," Papers 1604.07556,
    13. Rama Cont & Lakshithe Wagalath, 2016. "Institutional Investors And The Dependence Structure Of Asset Returns," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-37, March.
    14. Chen, Jingnan & Feng, Liming & Peng, Jiming, 2015. "Optimal deleveraging with nonlinear temporary price impact," European Journal of Operational Research, Elsevier, vol. 244(1), pages 240-247.
    15. D. Sornette, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models," Papers 1404.0243,
    16. Ibrahim Ekren & Ren Liu & Johannes Muhle-Karbe, 2015. "Optimal Rebalancing Frequencies for Multidimensional Portfolios," Papers 1510.05097,, revised Sep 2017.
    17. Emilio Said & Ahmed Bel Hadj Ayed & Alexandre Husson & Frédéric Abergel, 2018. "Market Impact: A systematic study of limit orders," Working Papers hal-01561128, HAL.
    18. Fabio Caccioli & Imre Kondor & Matteo Marsili & Susanne Still, 2016. "Liquidity Risk And Instabilities In Portfolio Optimization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-28, August.
    19. Lillo, Fabrizio & Pirino, Davide, 2015. "The impact of systemic and illiquidity risk on financing with risky collateral," Journal of Economic Dynamics and Control, Elsevier, vol. 50(C), pages 180-202.
    20. Hai-Chuan Xu & Zhi-Qiang Jiang & Wei-Xing Zhou, 2016. "Immediate price impact of a stock and its warrant: Power-law or logarithmic model?," Papers 1611.04091,

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