Multivariate Stochastic Volatility

The literature on multivariate stochastic volatility (MSV) models has developed significantly over the last few years. This paper reviews the substantial literature on specification, estimation and evaluation of MSV models. A wide range of MSV models is presented according to various categories, namely (i) asymmetric models; (ii) factor models; (iii) time-varying correlation models; and (iv) alternative MSV specifications, including models based on the matrix exponential transformation, Cholesky decomposition, Wishart autoregressive process, and the empirical range. Alternative methods of estimation, including quasi-maximum likelihood, simulated maximum likelihood, Monte Carlo likelihood, and Markov chain Monte Carlo methods, are discussed and compared. Various methods of diagnostic checking and model comparison are also examined.