We propose a multivariate dynamic intensity peaks-over-threshold model to capture extremes in multivariate return processes. The random occurrence of extremes is modeled by a multivariate dynamic intensity model, while temporal clustering of their size is captured by an autoregressive multiplicative error model. Applying the model to daily returns of three major stock indexes yields strong empirical support for a temporal clustering of both the occurrence and the size of extremes. Backtesting value-at-risk and expected shortfall forecasts shows that the consideration of clustering effects and of feedback between the magnitudes and the intensity of extremes results in better forecasts of risk.
