High volatility, thick tails and extreme value theory in value-at-risk estimation

Abstract

In this paper, the performance of the extreme value theory in value-at-risk calculations is compared to the performances of other well-known modeling techniques, such as GARCH, variance-covariance (Var-Cov) method and historical simulation in a volatile stock market. The models studied can be classified into two groups. The first group consists of GARCH(1, 1) and GARCH(1, 1)- t models which yield highly volatile quantile forecasts. The other group, consisting of historical simulation, Var-Cov approach, adaptive generalized Pareto distribution (GPD) and nonadaptive GPD models, leads to more stable quantile forecasts. The quantile forecasts of GARCH(1, 1) models are excessively volatile relative to the GPD quantile forecasts. This makes the GPD model be a robust quantile forecasting tool which is practical to implement and regulate for VaR measurements. © 2003 Elsevier B.V. All rights reserved