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The Value-at-Risk (VaR) is a widely used instrument in financial riskmanagement. The question of estimating the VaR of loss return distributions atextreme levels is an important question in financial applications, both fromoperational and regulatory perspectives; in particular, the dynamic estimationof extreme VaR given the recent past has received substantial attention. Wepropose here a two-step bias-reduced estimation methodology called GARCH-UGH(Unbiased Gomes-de Haan), whereby financial returns are first filtered using anAR-GARCH model, and then a bias-reduced estimator of extreme quantiles isapplied to the standardized residuals to estimate one-step ahead dynamicextreme VaR. Our results indicate that the GARCH-UGH estimates are moreaccurate than those obtained by combining conventional AR-GARCH filtering andextreme value estimates from the perspective of in-sample and out-of-samplebacktestings of historical daily returns on several financial time series.

GARCH-UGH: A bias-reduced approach for dynamic extreme Value-at-Risk estimation in financial time series