We propose a model that can capture the typical features of multivariate extreme events observed in financial time series, namely clustering behavior in magnitudes and arrival times of multivariate extreme events, and time-varying dependence. The model is developed in the framework of the peaks-over-threshold approach in extreme value theory and relies on a Poisson process with selfexciting intensity. We discuss the properties of the model, treat its estimation, deal with testing goodness-of-fit, and develop a simulation algorithm. The model is applied to return data of two stock markets and four major European banks.