Conditional ASGT-GARCH Approach to Value-at-Risk

Abstract

Most of the Value-at-Risk (VaR) models assume that asset returns are normally distributed, despite the fact that they are commonly known to be left skewed, fat-tailed and excess kurtosis. Forecasting VaR with misspecified model leads to the underestimation or overestimation of the true VaR. This paper proposes a new conditional model to forecast VaR by employing the alpha-skew generalized T (ASGT) distribution to GARCH models. ASGT distribution, introduced by Acitas et al. (Revista Colombiana de Estadistica 38(2):353–370, 2015), allows to model skewness, leptokurtosis and fat tail properties of conditional distribution of asset returns. ISE-100 index is used to examine the one-day-ahead VaR forecasting ability of the GARCH model under normal, Student’s t, generalized error, generalized T, skewed generalized T and ASGT innovation distributions. Empirical results show that the ASGT provides a superior fit to the conditional distribution of the log-returns followed by normal, Student’s t, generalized error, generalized T and skewed generalized T distributions. Moreover, for all confidence levels, all models tend to underestimate real market risk. Furthermore, the GARCH-based model, with ASGT error distribution, generates the most reliable VaR forecasts followed by other competitive models for a long position. As a result of this study, we conclude that the effects of skewness and fat-tails are more important in terms of forecasting true VaR than only the effect of fat-tails on VaR forecasts.