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Price Variations in a Stock Market with Many Agents

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Abstract

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 large, the market price is generally locked within the price range they define.

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File URL: http://cowles.econ.yale.edu/P/cd/d11a/d1132.pdf
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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1132.

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Length: 43 pages
Date of creation: Sep 1996
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Publication status: Published in Physica A: Statistical Mechanics and its Applications (December 1997), 246(3-4): 430–453
Handle: RePEc:cwl:cwldpp:1132

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  1. Grandmont, Jean-Michel, 1993. "Behavioral heterogeneity and Cournot oligopoly equilibrium," CEPREMAP Working Papers (Couverture Orange) 9305, CEPREMAP.
  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. repec:sfi:sfiwpa:9607120 is not listed on IDEAS
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