The study of interdependence and the strength of the relationship between finan-cial time series is a quite important area in the financial literature. Hence we discussed the relationships between the main stock indices. The multivariate distributions of returns we modelled basing on copula functions approach. In order to obtain some dynamics of multi-variate distributions we applied the hidden Markov chain. Additionally we assumed that the transition matrix of the Markov chain was dependent on some exogenous variables. The study shows that the volatility indices VIX and VSTOXX which were taken as exogenous variables improved model efficiency.