A new multivariate time series model with various attractive properties is motivated and studied. By extending the CCC model in several ways, it allows for all the primary stylized facts of financial asset returns, including volatility clustering, non-normality (excess kurtosis and asymmetry), and also dynamics in the dependency between assets over time. A fast EM-algorithm is developed for estimation. Each element of the vector return at time tt is endowed with a common univariate shock, interpretable as a common market factor. This leads to the new model being a hybrid of GARCH and stochastic volatility, but without the estimation problems associated with the latter, and being applicable in the multivariate setting for potentially large numbers of assets. A feasible technique which allows for multivariate option pricing is presented, along with an empirical illustration.