Instabilities in the price dynamics of a large number of financial assets are a clear sign of
systemic events. By investigating portfolios of highly liquid stocks, we find that there are 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.