Clustering financial time series is a recent topic of statistical literature with important fields of applications, in particular portfolio composition and risk evaluation. The risk is generally linked to the volatility of the asset, but its level of predictability also plays a basic role in investment decisions. In particular, the classification of a certain asset could be linked to its dependence on the volatility of a dominant market: movements in the volatility of the dominant market can provide similar movements in the volatility of the asset and its predictability would depend on the strength of this dependence. Working in a model based framework, we base the classification of the volatility of an asset not only on its volatility level, but also on the presence of spillover effects from a dominant market, such as the U.S. one, and on the similarity of the dynamics of the asset and the dominant market. The method is carried out using an extended version of the Multiplicative Error Model and is applied to a set of European assets.