  Instabilities in the price dynamics of a large number of financial assets are
a clear sign of systemic events. By investigating a set of 20 high cap stocks
traded at the Italian Stock Exchange, we find that there is a large number of
high frequency cojumps. We show that the dynamics of these jumps is described
neither by a multivariate Poisson nor by a multivariate Hawkes model. We
introduce a Hawkes one factor model which is able to capture simultaneously the
time clustering of jumps and the high synchronization of jumps across assets.
