Value-at-risk forecasts: a comparison analysis of extreme-value versus classical approaches

ABSTRACT This paper compares the performance of several different value-at-risk (VaR) forecast models: historical simulation, RiskMetrics and models based on extreme value theory. Both the parametric maximum likelihood and nonparametric Hill estimator, and the modified estimator of Dekkers, Einmahl and de Haan are applied to estimate the tail index of extreme-value models. Those VaR forecast models that satisfy criteria of both unconditional and conditional coverage have also been tested in terms of a quantile loss function. Among the approaches used in the study, the extreme-value model forecasts are found to outperform the classical historical simulation and RiskMetrics approaches.