We present a marked point process model for the excesses of a time series over a high threshold that combines Hawkes processes for the exceedances with generalized Pareto distribution for the marks (exceedance sizes). In a financial context, the conditional approach models intraday clustering of extremes of log-returns time series and is used to calculate instantaneous conditional VaR. The form of the process allows realistic models in which recent events affect the current intensity more than more distant ones, but it also allows the intensity to depend on the sizes of the events. The models are backtested on real data. The talk is based on joint work with James McGill.