A FLEXIBLE CLASS OF STOCHASTIC VOLATILITY MODELS OF THE DIFFUSION TYPE

Michael Sørensen

Abstract

A class of stochastic volatility models driven by Wiener processes will be presented. These models are analytically relatively tractable and have a flexible correlation structure. Any absolutely continuous, infinitely divisible probability distribution with finite variance can be obtained as marginal distribution of the volatility process. A particular example is the class of generalized inverse Gaussian distributions, for which approximately generalized hyperbolic returns are obtained. The gamma distribution and the inverse Gaussian distribution will be given particular attention. The models presented in the talk fit nicely into the framework of the prediction-based estimating functions introduced in Sørensen (2000) [Econometrics Journal, 3, 123 - 147]). Estimation of the model parameters by means of this method will be discussed. Also option pricing will be considered.