New parametrization of stochastic volatility models

The basic objective of this paper is to introduce a new parametrization and extension of stochastic volatility models where the diffusion of the stock return is generated by the shifted compound Poisson distribution. This new class generalizes the affine standard process and can be better adapted to several empirical characteristics of return data. The shifted compound Poisson Model is more flexible and is usually implemented to modeling negative and non negative continuous data with a discrete probability mass at zero. The proposed model parameters, based on the Bayesian analysis, have been estimated. Furthermore, the dispersion stochastic volatility ϕt which follows an infinite mixture inverse Gamma distribution is elaborated. The model’s performance has been analyzed with real data for its selection by varying the power parameter p in {0}∪(1,2). The paper also develops formal tools for comparing the basic standard stochastic volatility and the proposed model. Moreover, the proposed methodology is illustrated by analyzing four series of real indexes returns.