A point process approach to Value-at-Risk estimation

We consider the modelling of rare events in financial time series,and introduce a marked point process model for the excesses of thetime series over a high threshold that combines a self-exciting processfor the exceedances with a mark (size) dependent process. This allowsrealistic models for rare events, in which recent events affect the currentintensity for exceedances more than distant ones, but it also allows theintensity to depend on the marks of the events. Estimates of Value-at-Risk are derived for real datasets and backtested.