Before revision:  We show that the dynamics of these jumps is not described neither by a multivariate Poisson nor by a multivariate Hawkes model , which are unable to capture simultaneously the time clustering of jumps and the high synchronization of jumps across assets . We introduce a one factor model approach where both the factor and the idiosyncratic jump components are described by a Hawkes process. We introduce a robust calibration scheme which is able to distinguish systemic and idiosyncratic jumps and we show that the model reproduces very well the empirical behaviour of the jumps of the Italian stocks .
After revision:  We show that the dynamics of these jumps is not described neither by a multivariate Poisson nor by a multivariate Hawkes model , which are unable to capture simultaneously the time clustering of jumps and the high synchronization of jumps across assets .