Statistical properties of the volatility of price fluctuations
- 1 August 1999
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 60 (2), 1390-1400
- https://doi.org/10.1103/physreve.60.1390
Abstract
We study the statistical properties of volatility, measured by locally averaging over a time window T, the absolute value of price changes over a short time interval We analyze the S&P 500 stock index for the 13-year period Jan. 1984 to Dec. 1996. We find that the cumulative distribution of the volatility is consistent with a power-law asymptotic behavior, characterized by an exponent similar to what is found for the distribution of price changes. The volatility distribution retains the same functional form for a range of values of T. Further, we study the volatility correlations by using the power spectrum analysis. Both methods support a power law decay of the correlation function and give consistent estimates of the relevant scaling exponents. Also, both methods show the presence of a crossover at approximately days. In addition, we extend these results to the volatility of individual companies by analyzing a data base comprising all trades for the largest 500 U.S. companies over the two-year period Jan. 1994 to Dec. 1995.
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