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 Δt. We analyze the S&P 500 stock index for the 13year period Jan. 1984 to Dec. 1996. We find that the cumulative distribution of the volatility is consistent with a powerlaw asymptotic behavior, characterized by an exponent μ~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 twoyear period Jan. 1994 to Dec. 1995.
 Publication:

Physical Review E
 Pub Date:
 August 1999
 DOI:
 10.1103/PhysRevE.60.1390
 arXiv:
 arXiv:condmat/9903369
 Bibcode:
 1999PhRvE..60.1390L
 Keywords:

 89.90.+n;
 Other topics in areas of applied and interdisciplinary physics;
 Condensed Matter  Statistical Mechanics;
 Quantitative Finance  Statistical Finance
 EPrint:
 34 pages (Revtex preprint format), 17 figures, 47 references