Univariate Extreme Value Theory , GARCH and Measures of Risk

In this paper we combine ARMA-(asymmetric) GARCH and EVT methods, applying them to the estimation of extreme quantiles (i.e., beyond the 95%) of univariate portfolio risk factors. In addition to Value at Risk we consider the tail conditional expectation (or expected shortfall). A comparison is also made with methods based on conditional normality (e.g., RiskMetrics), conditional t-distribution as well as the empirical distribution function. The paper is partially self-contained as it details the ARMA-(asymmetric) GARCH model as well the GMM-estimator used. It introduces the most important theoretical results of univariate EVT, discusses risk measures on a general level as well as the notion of coherent measure of risk.