Modern approaches to financial time series aim to model in a multivariate framework the volatility of different indices or assets, which could influence each other, creating spillover effects. Furthermore, the integration of financial markets provides a similar dynamics (co-movement). We propose a new model for volatility vectors, belonging to the family of Multiplicative Error Models, which incorporates spillover and co-movement effects. By adopting an appropriate parameterization, it is possible to estimate this model even for high dimensional vectors of volatility. To reduce the number of unknown coefficients, we propose a 3-step model-based clustering procedure. The proposed model is applied to a set of seventeen world financial indices, providing a useful interpretation of spillover effects and co- movements. Furthermore, the proposed parameterization is compared with two alternatives, showing significantly better performance.