Extreme Returns, Tail Estimation and Value-at-Risk

Accurate prediction of extreme events are of primary importance in many financial ap-plications. 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. How-ever, 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.

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