Volatility in the Italian Stock Market: An Empirical Study

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.