Value-at-risk and extreme returns

Accurate prediction of extreme events are of primary importance in many financial applications. The properties of historical simulation and RiskMetrics techniques for computing Value-at-Risk (VaR) are compared with a method which involves modelling the tails of financial returns explicitly with a tail estimator. The methods are compared using a sample of U. S. stock returns. For predictions of low probability worst outcomes, RiskMetrics type analysis underpredicts while historical simulation overpredicts. However, the estimates obtained from applying the tail estimator are more accurate in the VaR prediction. This implies that capital requirements can be lower by doing VaR with the tail estimator.