title: Statistical properties of the volatility of price fluctuations.
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 deltat. 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 mu approximately 3, 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 1.5 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.
authors.affiliation: Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
authors.forename: Y
authors.initials: Y
authors.lastname: Liu
authors.forename: P
authors.initials: P
authors.lastname: Gopikrishnan
authors.forename: P
authors.initials: P
authors.lastname: Cizeau
authors.forename: M
authors.initials: M
authors.lastname: Meyer
authors.forename: C K
authors.initials: CK
authors.lastname: Peng
authors.forename: H E
authors.initials: HE
authors.lastname: Stanley