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Liquidity crisis, granularity of the order book and price fluctuations

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  • M. Cristelli
  • V. Alfi
  • L. Pietronero
  • A. Zaccaria

Abstract

We introduce a microscopic model for the dynamics of the order book to study how the lack of liquidity influences price fluctuations. We use the average density of the stored orders (granularity $g$) as a proxy for liquidity. This leads to a Price Impact Surface which depends on both volume $\omega$ and $g$. The dependence on the volume (averaged over the granularity) of the Price Impact Surface is found to be a concave power law function $ _g\sim\omega^\delta$ with $\delta\approx 0.59$. Instead the dependence on the granularity is $\phi(\omega,g|\omega)\sim g^\alpha$ with $\alpha\approx-1$, showing a divergence of price fluctuations in the limit $g\to 0$. Moreover, even in intermediate situations of finite liquidity, this effect can be very large and it is a natural candidate for understanding the origin of large price fluctuations.
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Suggested Citation

  • M. Cristelli & V. Alfi & L. Pietronero & A. Zaccaria, 2010. "Liquidity crisis, granularity of the order book and price fluctuations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 73(1), pages 41-49, January.
    • Handle: RePEc:spr:eurphb:v:73:y:2010:i:1:p:41-49
    DOI: 10.1140/epjb/e2009-00353-6
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    References listed on IDEAS

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    1. Armand Joulin & Augustin Lefevre & Daniel Grunberg & Jean-Philippe Bouchaud, 2008. "Stock price jumps: news and volume play a minor role," Papers 0803.1769, arXiv.org.
    2. Mike, Szabolcs & Farmer, J. Doyne, 2008. "An empirical behavioral model of liquidity and volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 200-234, January.
    3. Jean-Philippe Bouchaud & J. Doyne Farmer & Fabrizio Lillo, 2008. "How markets slowly digest changes in supply and demand," Papers 0809.0822, arXiv.org.
    4. Fabrizio Lillo & J. Doyne Farmer & Rosario N. Mantegna, 2002. "Single Curve Collapse of the Price Impact Function for the New York Stock Exchange," Papers cond-mat/0207428, arXiv.org.
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    Cited by:

    1. Federico Garzarelli & Matthieu Cristelli & Andrea Zaccaria & Luciano Pietronero, 2011. "Memory effects in stock price dynamics: evidences of technical trading," Papers 1110.5197, arXiv.org.
    2. James Paulin & Anisoara Calinescu & Michael Wooldridge, 2018. "Understanding Flash Crash Contagion and Systemic Risk: A Micro-Macro Agent-Based Approach," Papers 1805.08454, arXiv.org.
    3. Kononovicius, Aleksejus & Ruseckas, Julius, 2019. "Order book model with herd behavior exhibiting long-range memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 171-191.
    4. Iris Lucas & Michel Cotsaftis & Cyrille Bertelle, 2017. "Heterogeneity and Self-Organization of Complex Systems Through an Application to Financial Market with Multiagent Systems," Post-Print hal-02114933, HAL.
    5. Hernández, Juan Antonio & Benito, Rosa Marı´a & Losada, Juan Carlos, 2012. "An adaptive stochastic model for financial markets," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 899-908.
    6. Roberto Mota Navarro & Francois Leyvraz & Hern'an Larralde, 2023. "Dynamical properties of volume at the spread in the Bitcoin/USD market," Papers 2304.01907, arXiv.org, revised May 2023.
    7. Paulin, James & Calinescu, Anisoara & Wooldridge, Michael, 2019. "Understanding flash crash contagion and systemic risk: A micro–macro agent-based approach," Journal of Economic Dynamics and Control, Elsevier, vol. 100(C), pages 200-229.
    8. Aleksejus Kononovicius & Julius Ruseckas, 2018. "Order book model with herd behavior exhibiting long-range memory," Papers 1809.02772, arXiv.org, revised Apr 2019.

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