Universal Behavior of Extreme Price Movements in Stock Markets |
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| Authors: | Miguel A Fuentes Austin Gerig Javier Vicente |
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| Institution: | 1. Santa Fe Institute, Santa Fe, New Mexico, United States of America.; 2. Center for Advanced Studies in Ecology and Biodiversity, Pontificia Universidad Católica de Chile, Santiago, Chile.; 3. Statistical and Interdisciplinary Physics Group, Instituto Balseiro and Consejo Nacional de Investigaciones Científicas y Técnicas, Bariloche, Argentina.; 4. School of Finance and Economics, University of Technology, Sydney, Australia.;University of East Piedmont, Italy |
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| Abstract: | Many studies assume stock prices follow a random process known as geometric Brownian motion. Although approximately correct, this model fails to explain the frequent occurrence of extreme price movements, such as stock market crashes. Using a large collection of data from three different stock markets, we present evidence that a modification to the random model—adding a slow, but significant, fluctuation to the standard deviation of the process—accurately explains the probability of different-sized price changes, including the relative high frequency of extreme movements. Furthermore, we show that this process is similar across stocks so that their price fluctuations can be characterized by a single curve. Because the behavior of price fluctuations is rooted in the characteristics of volatility, we expect our results to bring increased interest to stochastic volatility models, and especially to those that can produce the properties of volatility reported here. |
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