  We study the volatility of the MIB30-stock-index high-frequency data from
November 28, 1994 through September 15, 1995. Our aim is to empirically
characterize the volatility random walk in the framework of continuous-time
finance. To this end, we compute the index volatility by means of the
log-return standard deviation. We choose an hourly time window in order to
investigate intraday properties of volatility. A periodic component is found
for the hourly time window, in agreement with previous observations.
Fluctuations are studied by means of detrended fluctuation analysis, and we
detect long-range correlations. Volatility values are log-stable distributed.
We discuss the implications of these results for stochastic volatility
modelling.
