  We study the exponential Ornstein-Uhlenbeck stochastic volatility model and
observe that the model shows a multiscale behavior in the volatility
autocorrelation. It also exhibits a leverage correlation and a probability
profile for the stationary volatility which are consistent with market
observations. All these features make the model quite appealing since it
appears to be more complete than other stochastic volatility models also based
on a two-dimensional diffusion. We finally present an approximate solution for
the return probability density designed to capture the kurtosis and skewness
effects.
