Exchangeability, extreme returns and Value-at-Risk forecasts

In this paper, we propose a new approach to extreme value modelling for the forecasting of Value-at-Risk (VaR). In particular, the block maxima and the peaks-over-threshold methods are generalised to exchangeable random sequences. This caters for the dependencies, such as serial autocorrelation, of financial returns observed empirically. In addition, this approach allows for parameter variations within each VaR estimation window. Empirical prior distributions of the extreme value parameters are attained by using resampling procedures. We compare the results of our VaR forecasts to that of the unconditional extreme value theory (EVT) approach and the conditional GARCH-EVT model for robust conclusions.