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

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

    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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    File URL: http://arxiv.org/pdf/1105.1694
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1105.1694.

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    Date of creation: May 2011
    Date of revision: Nov 2011
    Publication status: Published in Physical Review X 1, 021006 (2011)
    Handle: RePEc:arx:papers:1105.1694

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    References

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    1. Eric Smith & J. Doyne Farmer & Laszlo Gillemot & Supriya Krishnamurthy, 2002. "Statistical theory of the continuous double auction," Papers cond-mat/0210475, arXiv.org.
    2. J. Doyne Farmer & Laszlo Gillemot & Fabrizio Lillo & Szabolcs Mike & Anindya Sen, 2004. "What really causes large price changes?," Quantitative Finance, Taylor & Francis Journals, vol. 4(4), pages 383-397.
    3. B. Tóth & F. Lillo & J. D. Farmer, 2010. "Segmentation algorithm for non-stationary compound Poisson processes," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 78(2), pages 235-243, November.
    4. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2006. "Institutional Investors and Stock Market Volatility," The Quarterly Journal of Economics, MIT Press, vol. 121(2), pages 461-504, May.
    5. Albert J. Menkveld, 2011. "High Frequency Trading and the New-Market Makers," Tinbergen Institute Discussion Papers 11-076/2/DSF21, Tinbergen Institute, revised 15 Aug 2011.
    6. Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2003. "Fluctuations and response in financial markets: the subtle nature of `random' price changes," Papers cond-mat/0307332, arXiv.org, revised Aug 2003.
    7. George C. Chacko & Jakub W. Jurek & Erik Stafford, 2008. "The Price of Immediacy," Journal of Finance, American Finance Association, vol. 63(3), pages 1253-1290, 06.
    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, arXiv.org.
    9. Lillo Fabrizio & Farmer J. Doyne, 2004. "The Long Memory of the Efficient Market," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(3), pages 1-35, September.
    10. Jean-Philippe Bouchaud & J. Doyne Farmer & Fabrizio Lillo, 2008. "How markets slowly digest changes in supply and demand," Papers 0809.0822, arXiv.org.
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    Cited by:
    1. Bence Toth & Imon Palit & Fabrizio Lillo & J. Doyne Farmer, 2011. "Why is order flow so persistent?," Papers 1108.1632, arXiv.org.
    2. D. Sornette, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models," Papers 1404.0243, arXiv.org.
    3. 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.
    4. Ludovic Moreau & Johannes Muhle-Karbe & H. Mete Soner, 2014. "Trading with Small Price Impact," Papers 1402.5304, arXiv.org.

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