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Price Variations in a Stock Market with Many Agents

  • P. Bak
  • M. Paczuski
  • M. Shubik

Large variations in stock prices happen with sufficient frequency to raise doubts about existing models, which all fail to account for non-Gaussian statistics. We construct simple models of a stock market, and argue that the large variations may be due to a crowd effect, where agents imitate each other's behavior. The variations over different time scales can be related to each other in a systematic way, similar to the Levy stable distribution proposed by Mandelbrot to describe real market indices. In the simplest, least realistic case, exact results for the statistics of the variations are derived by mapping onto a model of diffusing and annihilating particles, which has been solved by quantum field theory methods. When the agents imitate each other and respond to recent market volatility, different scaling behavior is obtained. In this case the statistics of price variations is consistent with empirical observations. The interplay between "rational" traders whose behavior is derived from fundamental analysis of the stock, including dividends, and "noise traders", whose behavior is governed solely by studying the market dynamics, is investigated. When the relative number of rational traders is small, "bubbles" often occur, where the market price moves outside the range justified by fundamental market analysis. When the number of rational traders is larger, the market price is generally locked within the price range they define.

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Paper provided by Santa Fe Institute in its series Working Papers with number 96-09-075.

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Date of creation: Sep 1996
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Handle: RePEc:wop:safiwp:96-09-075
Contact details of provider: Postal: 1399 Hyde Park Road, Santa Fe, New Mexico 87501
Web page: http://www.santafe.edu/sfi/publications/working-papers.html

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  1. Jean-Michel Grandmont, 1993. "Behavioral Heterogeneity and Cournot Oligopoly Equilibrium," Cowles Foundation Discussion Papers 1044, Cowles Foundation for Research in Economics, Yale University.
  2. Gale, Douglas & Rosenthal, Robert W., 1999. "Experimentation, Imitation, and Stochastic Stability," Journal of Economic Theory, Elsevier, vol. 84(1), pages 1-40, January.
  3. Alain Arneodo & Jean-Philippe Bouchaud & Rama Cont & Jean-Francois Muzy & Marc Potters & Didier Sornette, 1996. "Comment on "Turbulent cascades in foreign exchange markets"," Science & Finance (CFM) working paper archive 9607120, Science & Finance, Capital Fund Management.
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