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Random walks, liquidity molasses and critical response in financial markets

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  • Jean-Philippe Bouchaud
  • Julien Kockelkoren
  • Marc Potters

Abstract

Stock prices are observed to be random walks in time despite a strong, long-term memory in the signs of trades (buys or sells). Lillo and Farmer have recently suggested that these correlations are compensated by opposite long-ranged fluctuations in liquidity, with an otherwise permanent market impact, challenging the scenario proposed in Quantitative Finance, 2004, 4, 176, where the impact is instead transient, with a power-law decay in time. The exponent of this decay is precisely tuned to a critical value, ensuring simultaneously that prices are diffusive on long time scales and that the impact function is nearly lag independent. We provide new analysis of empirical data that confirm and make more precise our previous claims. We show that the power-law decay of the bare impact function comes both from an excess flow of limit order opposite to the market order flow, and to a systematic anti-correlation of the bid-ask motion between trades, two effects that create a 'liquidity molasses' which dampens market volatility.

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Bibliographic Info

Article provided by Taylor and Francis Journals in its journal Quantitative Finance.

Volume (Year): 6 (2006)
Issue (Month): 2 ()
Pages: 115-123

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Handle: RePEc:taf:quantf:v:6:y:2006:i:2:p:115-123

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References

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  1. J. Doyne Farmer & Fabrizio Lillo, 2003. "On the origin of power law tails in price fluctuations," Papers cond-mat/0309416, arXiv.org, revised Jan 2004.
  2. Eric Smith & J Doyne Farmer & Laszlo Gillemot & Supriya Krishnamurthy, 2003. "Statistical theory of the continuous double auction," Quantitative Finance, Taylor and Francis Journals, vol. 3(6), pages 481-514.
  3. Lux, T. & M. Marchesi, . "Volatility Clustering in Financial Markets: A Micro-Simulation of Interacting Agents," Discussion Paper Serie B 437, University of Bonn, Germany, revised Jul 1998.
  4. Parameswaran Gopikrishnan & Vasiliki Plerou & Luis A. Nunes Amaral & Martin Meyer & H. Eugene Stanley, 1999. "Scaling of the distribution of fluctuations of financial market indices," Papers cond-mat/9905305, arXiv.org.
  5. Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2003. "Fluctuations and response in financial markets: the subtle nature of `random' price changes," Science & Finance (CFM) working paper archive 0307332, Science & Finance, Capital Fund Management.
  6. Hasbrouck, Joel, 1991. " Measuring the Information Content of Stock Trades," Journal of Finance, American Finance Association, vol. 46(1), pages 179-207, March.
  7. Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2004. "Fluctuations and response in financial markets: the subtle nature of 'random' price changes," Quantitative Finance, Taylor and Francis Journals, vol. 4(2), pages 176-190.
  8. Wyart, Matthieu & Bouchaud, Jean-Philippe, 2007. "Self-referential behaviour, overreaction and conventions in financial markets," Journal of Economic Behavior & Organization, Elsevier, vol. 63(1), pages 1-24, May.
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  12. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Science & Finance (CFM) working paper archive 0203511, Science & Finance, Capital Fund Management.
  13. Shiller, Robert J, 1981. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," American Economic Review, American Economic Association, vol. 71(3), pages 421-36, June.
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  15. J. Doyne Farmer & Laszlo Gillemot & Fabrizio Lillo & Szabolcs Mike & Anindya Sen, 2003. "What really causes large price changes?," Papers cond-mat/0312703, arXiv.org, revised Apr 2004.
  16. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Quantitative Finance, Taylor and Francis Journals, vol. 2(4), pages 251-256.
  17. Vasiliki Plerou & Parameswaran Gopikrishnan & Xavier Gabaix & H. Eugene Stanley, 2004. "On the Origin of Power-Law Fluctuations in Stock Prices," Papers cond-mat/0403067, arXiv.org.
  18. Potters, Marc & Bouchaud, Jean-Philippe, 2003. "More statistical properties of order books and price impact," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 133-140.
  19. D. Challet & A. Chessa & M. Marsili & Y-C. Zhang, 2001. "From Minority Games to real markets," Quantitative Finance, Taylor and Francis Journals, vol. 1(1), pages 168-176.
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  21. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor and Francis Journals, vol. 1(2), pages 223-236.
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Citations

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Cited by:
  1. Carl Chiarella & Giulia Iori & Josep Perello, 2007. "The Impact of Heterogeneous Trading Rules on the Limit Order Book and Order Flows," Papers 0711.3581, arXiv.org.
  2. Szabolcs Mike & J. Doyne Farmer, 2007. "An empirical behavioral model of liquidity and volatility," Papers 0709.0159, arXiv.org.
  3. R\'emy Chicheportiche & Jean-Philippe Bouchaud, 2012. "The fine-structure of volatility feedback," Papers 1206.2153, arXiv.org.
  4. Steffen Bohn, 2011. "The slippage paradox," Papers 1103.2214, arXiv.org.
  5. Enzo Busseti & Fabrizio Lillo, 2012. "Calibration of optimal execution of financial transactions in the presence of transient market impact," Papers 1206.0682, arXiv.org.
  6. Steffen Bohn, 2011. "The slippage paradox," Working Papers hal-00574268, HAL.
  7. Matthieu Wyart & Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters & Michele Vettorazzo, 2006. "Relation between Bid-Ask Spread, Impact and Volatility in Double Auction Markets," Papers physics/0603084, arXiv.org, revised Mar 2007.
  8. Bence Toth & Imon Palit & Fabrizio Lillo & J. Doyne Farmer, 2011. "Why is order flow so persistent?," Papers 1108.1632, arXiv.org.
  9. A. Zaccaria & M. Cristelli & V. Alfi & F. Ciulla & L. Pietronero, 2009. "Asymmetric statistics of order books: The role of discreteness and evidence for strategic order placement," Papers 0906.1387, arXiv.org, revised May 2010.
  10. Khalil al Dayri & Emmanuel Bacry & Jean-Francois Muzy, 2010. "The nature of price returns during periods of high market activity," Papers 1010.4226, arXiv.org, revised Oct 2010.
  11. B. T�th & Z. Eisler & F. Lillo & J. Kockelkoren & J.-P. Bouchaud & J.D. Farmer, 2012. "How does the market react to your order flow?," Quantitative Finance, Taylor and Francis Journals, vol. 12(7), pages 1015-1024, May.
  12. J. Doyne Farmer & Austin Gerig & Fabrizio Lillo & Szabolcs Mike, 2006. "Market efficiency and the long-memory of supply and demand: Is price impact variable and permanent or fixed and temporary?," Papers physics/0602015, arXiv.org.
  13. Wyart, Matthieu & Bouchaud, Jean-Philippe, 2007. "Self-referential behaviour, overreaction and conventions in financial markets," Journal of Economic Behavior & Organization, Elsevier, vol. 63(1), pages 1-24, May.
  14. Jean-Philippe Bouchaud, 2011. "Panel Statement: The endogenous dynamics of markets: price impact and feedback loops," Chapters, European Central Bank.

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