Financial crises dramatically highlight the need for a reliable quantitative analysis of real market data, able to guide the formulation of realistic theoretical models for the nancial dynamics and the development of eective tools to measure and manage risk. In recent years great attention has been devoted to stochastic volatility models able to capture the random nature of volatility. Our attention focuses on processes which have been proven to provide a realistic description of historical time series, as it is the case for the exponential Ornstein- Uhlenbeck model, and we present results concerning a new model able to well describe the empirical volatility distribution and to better capture its tail behaviour with respect to the log-normal density. We review some of the analytical and numerical results concerning the probabilistic characterization of these models. Within the mathematical framework of the generalized Fourier transform, we discuss how to eciently price derivatives and to compute the level of market risk exposition when the characteristic function of the process is known in closed form. We provide several numerical evidences, both Monte Carlo and based on real data sets, proving the feasability of the proposed approach.