Liquidity crisis, granularity of the order book and price fluctuations

The European Physical Journal B volume 73, pages41–49(2010)Cite this article

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 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.

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References

  1. 1.

    M. Goodfriend, R.G. King, The New Neoclassical Synthesis (NBER Macroeconomics Annual, 1997)

  2. 2.

    J. Hasbrouck, Empirical Market Microstructure (Oxford University Press, 2007)

  3. 3.

    L. Harris, Trading and Exchanges (Oxford University Press, 2003)

  4. 4.

    F. Lillo, J.D. Farmer, Fluc. Noise Lett. 5, 209 (2005)

    Article  Google 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)

  6. 6.

    P. Weber, B. Rosenow, Quant. Fin. 6, 7 (2006)

    MATH  Article  MathSciNet  Google Scholar 

  7. 7.

    J.D. Farmer, L. Gillemot, F. Lillo, S. Mike, A. Sen, Quant. Fin. 4, 383 (2004)

    Article  Google Scholar 

  8. 8.

    J.D. Farmer, A. Gerig, F. Lillo, S. Mike, Quant. Fin. 6, 107 (2006)

    MATH  Article  MathSciNet  Google Scholar 

  9. 9.

    J.-P. Bouchaud, J. Kockelkoren, M. Potters, Quant. Fin. 6, 115 (2004)

    Article  MathSciNet  Google 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)

  12. 12.

    J.-P. Bouchaud, Nature 455, 176 (2008)

    Article  Google Scholar 

  13. 13.

    M. Marsili, Eroding market stability by proliferation of financial instruments. Available at SSRN: http://ssrn.com/abstract=1305174 (2008)

  14. 14.

    J.-P. Bouchaud, M. Mezard, M. Potters, Quant. Fin. 2, 251 (2002)

    Article  Google Scholar 

  15. 15.

    M. Potters, J.-P. Bouchaud, Physica A 324, 133 (2003)

    MATH  Article  ADS  Google Scholar 

  16. 16.

    M. Wyart, J.-P. Bouchaud, J. Kockelkoren, M. Potters, M. Vettorazzo, Quant. Fin. 8, 41 (2008)

    MATH  Article  Google Scholar 

  17. 17.

    F. Slanina, Eur. Phys. J. B 61, 225 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  18. 18.

    D. Challet, R. Stinchcombe, Quant. Fin. 3, 155 (2003)

    Article  Google Scholar 

  19. 19.

    M.G. Daniels, J.D. Farmer, L. Gillemot, G. Iori, E. Smith, Phys. Rev. Lett. 90, 108102 (2003)

    Article  ADS  Google Scholar 

  20. 20.

    E. Smith, J.D. Farmer, L. Gillemot, S. Krishnamurthy, Quant. Fin. 3, 481 (2003)

    Article  MathSciNet  Google Scholar 

  21. 21.

    S. Mike, J.D. Farmer, J. Econ. Dyn. Control 32, 200 (2008)

    Article  Google Scholar 

  22. 22.

    J.D. Farmer, P. Patelli, I.I. Zovko, PNAS 102, 2254 (2005)

    Article  ADS  Google Scholar 

  23. 23.

    V. Alfi, L. Pietronero, A. Zaccaria, EPL 86, 58003 (2009)

    Article  ADS  Google Scholar 

  24. 24.

    V. Alfi, M. Cristelli, L. Pietronero, A. Zaccaria, Eur. Phys. J. B 67, 385 (2009)

    Article  ADS  Google Scholar 

  25. 25.

    V. Alfi, M. Cristelli, L. Pietronero, A. Zaccaria, Eur. Phys. J. B 67, 399 (2009)

    Article  ADS  Google Scholar 

  26. 26.

    V. Alfi, M. Cristelli, L. Pietronero, A. Zaccaria, J. Stat. P03016 (2009)

  27. 27.

    V. Alfi, M. Cristelli, L. Pietronero, A. Zaccaria (preprint)

  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)

    Article  ADS  Google 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)

  31. 31.

    J.D. Farmer, F. Lillo, Quant. Fin. 4, 7 (2004)

    Article  Google Scholar 

  32. 32.

    V. Plerou, P. Gopikrishnan, X. Gabaix, H.E. Stanley, Phys. Rev. E 324, 66 (2002)

    Google Scholar 

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Author information

Affiliations

  1. Dip. di Fisica, Università “La Sapienza”, P.le A. Moro 2, 00185, Roma, Italy

    M. Cristelli, V. Alfi, L. Pietronero & A. Zaccaria

  2. Centro “E. Fermi”, Compendio Viminale, 00184, Roma, Italy

    V. Alfi

  3. ISC-CNR, V. dei Taurini 19, 00185, Roma, Italy

    L. Pietronero

Authors
  1. M. Cristelli
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  2. V. Alfi
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  3. L. Pietronero
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  4. A. Zaccaria
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Correspondence to M. Cristelli.

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Cristelli, M., Alfi, V., Pietronero, L. et al. Liquidity crisis, granularity of the order book and price fluctuations. Eur. Phys. J. B 73, 41–49 (2010). https://doi.org/10.1140/epjb/e2009-00353-6

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Keywords

  • Price Variation
  • Limit Order
  • Price Impact
  • Order Book
  • Impact Surface