The European Physical Journal B

, Volume 73, Issue 1, pp 41–49 | Cite as

Liquidity crisis, granularity of the order book and price fluctuations

  • M. CristelliEmail author
  • V. Alfi
  • L. Pietronero
  • A. Zaccaria
Topical Issue on Interdisciplinary Applications of Physics in Economics and Finance


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 ω 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 〈φ(ω,g)〉g∼ωδ with δ≈0.59. Instead the dependence on the granularity is φ(ω,g|ω)∼gα with α≈-1, showing a divergence of price fluctuations in the limit g→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.


Price Variation Limit Order Price Impact Order Book Impact Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Goodfriend, R.G. King, The New Neoclassical Synthesis (NBER Macroeconomics Annual, 1997)Google Scholar
  2. 2.
    J. Hasbrouck, Empirical Market Microstructure (Oxford University Press, 2007)Google Scholar
  3. 3.
    L. Harris, Trading and Exchanges (Oxford University Press, 2003)Google Scholar
  4. 4.
    F. Lillo, J.D. Farmer, Fluc. Noise Lett. 5, 209 (2005)CrossRefGoogle Scholar
  5. 5.
    A. Joulin, A. Lefevre, D. Grunberg, J.-P. Bouchaud, Stock price jumps: news and volume play a minor role, e-print [physics.soc-ph] arXiv:0803.1769v1 (2008)Google Scholar
  6. 6.
    P. Weber, B. Rosenow, Quant. Fin. 6, 7 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    J.D. Farmer, L. Gillemot, F. Lillo, S. Mike, A. Sen, Quant. Fin. 4, 383 (2004)CrossRefGoogle Scholar
  8. 8.
    J.D. Farmer, A. Gerig, F. Lillo, S. Mike, Quant. Fin. 6, 107 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    J.-P. Bouchaud, J. Kockelkoren, M. Potters, Quant. Fin. 6, 115 (2004)CrossRefMathSciNetGoogle Scholar
  10. 10.
    J.-P. Bouchaud, J.D. Farmer, F. Lillo, How Markets Slowly Digest Changes in Supply and Demand (Elsevier: Academic Press, 2008)Google Scholar
  11. 11.
    M. Gallegati, L. Pietronero, The Economists’ Voice (2008)Google Scholar
  12. 12.
    J.-P. Bouchaud, Nature 455, 176 (2008)CrossRefGoogle Scholar
  13. 13.
    M. Marsili, Eroding market stability by proliferation of financial instruments. Available at SSRN: (2008)
  14. 14.
    J.-P. Bouchaud, M. Mezard, M. Potters, Quant. Fin. 2, 251 (2002)CrossRefGoogle Scholar
  15. 15.
    M. Potters, J.-P. Bouchaud, Physica A 324, 133 (2003)zbMATHCrossRefADSGoogle Scholar
  16. 16.
    M. Wyart, J.-P. Bouchaud, J. Kockelkoren, M. Potters, M. Vettorazzo, Quant. Fin. 8, 41 (2008)zbMATHCrossRefGoogle Scholar
  17. 17.
    F. Slanina, Eur. Phys. J. B 61, 225 (2008)CrossRefMathSciNetADSGoogle Scholar
  18. 18.
    D. Challet, R. Stinchcombe, Quant. Fin. 3, 155 (2003)CrossRefGoogle Scholar
  19. 19.
    M.G. Daniels, J.D. Farmer, L. Gillemot, G. Iori, E. Smith, Phys. Rev. Lett. 90, 108102 (2003)CrossRefADSGoogle Scholar
  20. 20.
    E. Smith, J.D. Farmer, L. Gillemot, S. Krishnamurthy, Quant. Fin. 3, 481 (2003)CrossRefMathSciNetGoogle Scholar
  21. 21.
    S. Mike, J.D. Farmer, J. Econ. Dyn. Control 32, 200 (2008)CrossRefGoogle Scholar
  22. 22.
    J.D. Farmer, P. Patelli, I.I. Zovko, PNAS 102, 2254 (2005)CrossRefADSGoogle Scholar
  23. 23.
    V. Alfi, L. Pietronero, A. Zaccaria, EPL 86, 58003 (2009)CrossRefADSGoogle Scholar
  24. 24.
    V. Alfi, M. Cristelli, L. Pietronero, A. Zaccaria, Eur. Phys. J. B 67, 385 (2009)CrossRefADSGoogle Scholar
  25. 25.
    V. Alfi, M. Cristelli, L. Pietronero, A. Zaccaria, Eur. Phys. J. B 67, 399 (2009)CrossRefADSGoogle Scholar
  26. 26.
    V. Alfi, M. Cristelli, L. Pietronero, A. Zaccaria, J. Stat. P03016 (2009)Google Scholar
  27. 27.
    V. Alfi, M. Cristelli, L. Pietronero, A. Zaccaria (preprint)Google Scholar
  28. 28.
    J.-P. Bouchaud, Y. Gefen, M. Potters, M. Wyart, Quant. Fin. 4, 176 (2004)Google Scholar
  29. 29.
    F. Lillo, S. Mike, J.D. Farmer, Phys. Rev. E 71, 066122 (2005)CrossRefADSGoogle Scholar
  30. 30.
    F. Lillo, J.D. Farmer, R.N. Mantegna, Single curve collapse of price impact function for the New York Stock Exchange, e-print: arXiv:cond-mat/0207428 (2002)Google Scholar
  31. 31.
    J.D. Farmer, F. Lillo, Quant. Fin. 4, 7 (2004)CrossRefGoogle Scholar
  32. 32.
    V. Plerou, P. Gopikrishnan, X. Gabaix, H.E. Stanley, Phys. Rev. E 324, 66 (2002)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • M. Cristelli
    • 1
    Email author
  • V. Alfi
    • 1
    • 2
  • L. Pietronero
    • 1
    • 3
  • A. Zaccaria
    • 1
  1. 1.Dip. di Fisica, Università “La Sapienza”RomaItaly
  2. 2.Centro “E. Fermi”, Compendio ViminaleRomaItaly
  3. 3.ISC-CNR, V. dei Taurini 19RomaItaly

Personalised recommendations