A Multivariate Ornstein-Uhlenbeck Type Stochastic Volatility Model

Using positive semidefinite processes of Ornstein-Uhlenbeck type a multivariate Ornstein-Uhlenbeck (OU) type stochastic volatility model is introduced. We derive many important statistical and probabilistic properties, e.g. the complete second order structure and a state-space representation. Noteworthy, many of our results are shown to be valid for the more general class of multivariate stochastic volatility models, which are driven by a stationary and square-integrable covariance matrix process. For the OU type stochastic volatility our results enable estimation and filtering of the volatility which we finally demonstrate with a short empirical illustration of our model.