Multivariate stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck processes: A quasi-likelihood approach

This paper extends the ordinary quasi-likelihood estimator for stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck (OU) processes to vector processes. Despite the fact that multivariate modeling of asset returns is essential for portfolio optimization and risk management -- major areas of financial analysis -- the literature on multivariate modeling of asset prices in continuous time is sparse, both with regard to theoretical and applied results. This paper uses non-Gaussian OU-processes as building blocks for multivariate models for high frequency financial data. The OU framework allows exact discrete time transition equations that can be represented on a linear state space form. We show that a computationally feasible quasi-likelihood function can be constructed by means of the Kalman filter also in the case of high-dimensional vector processes. The framework is applied to Euro/NOK and US Dollar/NOK exchange rate data for the period 2.1.1989-4.2.2010.