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Fluctuations and response in financial markets: the subtle nature of `random' price changes

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  • Jean-Philippe Bouchaud

    (Science & Finance, Capital Fund Management
    CEA Saclay;)

  • Yuval Gefen

    (Weizmann Institute)

  • Marc Potters

    (Science & Finance, Capital Fund Management)

  • Matthieu Wyart

    (CEA Saclay;)

Abstract

Using Trades and Quotes data from the Paris stock market, we show that the random walk nature of traded prices results from a very delicate interplay between two opposite tendencies: strongly correlated market orders that lead to super-diffusion (or persistence), and mean reverting limit orders that lead to sub-diffusion (or anti-persistence). We define and study a model where the price, at any instant, is the result of the impact of all past trades, mediated by a non constant `propagator' in time that describes the response of the market to a single trade. Within this model, the market is shown to be, in a precise sense, at a critical point, where the price is purely diffusive and the average response function almost constant. We find empirically, and discuss theoretically, a fluctuation-response relation. We discuss the information content of each trade, and find that it is on average very small.

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Bibliographic Info

Paper provided by Science & Finance, Capital Fund Management in its series Science & Finance (CFM) working paper archive with number 0307332.

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Date of creation: Jul 2003
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Publication status: Published in Quantitative Finance 4 (April 2004) 176-190
Handle: RePEc:sfi:sfiwpa:0307332

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  1. Eric Smith & J Doyne Farmer & Laszlo Gillemot & Supriya Krishnamurthy, 2003. "Statistical theory of the continuous double auction," Quantitative Finance, Taylor & Francis Journals, vol. 3(6), pages 481-514.
  2. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 251-256.
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  6. 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.
  7. 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.
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  9. Bak, P. & Paczuski, M. & Shubik, M., 1997. "Price variations in a stock market with many agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 430-453.
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  11. Jean-Philippe Bouchaud & Rama Cont, 1998. "A Langevin approach to stock market fluctuations and crashes," Science & Finance (CFM) working paper archive 500027, Science & Finance, Capital Fund Management.
  12. Vasiliki Plerou & Parameswaran Gopikrishnan & Xavier Gabaix & H. Eugene Stanley, 2001. "Quantifying Stock Price Response to Demand Fluctuations," Papers cond-mat/0106657, arXiv.org.
  13. 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.
  14. Challet, Damien & Stinchcombe, Robin, 2001. "Analyzing and modeling 1+1d markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 300(1), pages 285-299.
  15. Frantisek Slanina, 2001. "Mean-field approximation for a limit order driven market model," Papers cond-mat/0104547, arXiv.org, revised Aug 2001.
  16. J-P. Bouchaud, 2001. "Power laws in economics and finance: some ideas from physics," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 105-112.
  17. Damien Challet & Robin Stinchcombe, 2003. "Non-constant rates and over-diffusive prices in a simple model of limit order markets," Quantitative Finance, Taylor & Francis Journals, vol. 3(3), pages 155-162.
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  1. What's Efficient About the Efficient Markets Hypothesis?
    by Mark Buchanan in The Physics of Finance on 2011-05-23 12:01:00
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