  We compare systematically several classes of stochastic volatility models of
stock market fluctuations. We show that the long-time return distribution is
either Gaussian or develops a power-law tail, while the short-time return
distribution has generically a stretched-exponential form, but can assume also
an algebraic decay, in the family of models which we call ``GARCH''-type. The
intermediate regime is found in the exponential Ornstein-Uhlenbeck process. We
calculate also the decay of the autocorrelation function of volatility.
