Asymmetric GARCH Value-at-Risk over MSCI in Financial Crisis

This paper uses four asymmetric generalized autoregressive conditional heteroskedasticity (GARCH) models, which are GJR-GARCH, NA-GARCH, Threshold GARCH (T-GARCH), and AV-GARCH to compare their performance on value-at-risk (VaR) forecasting to the symmetric GARCH model. In addition, we adopt four different mean equations which are autoregressive moving average (ARMA[1,1]), AR(1), MA(1), and “in-mean” to find out a more appropriate GARCH method in estimating VaR of MSCI World Index in financial crisis. We pick up 900 daily information of MSCI World Index from 2006 to 2009. We find that GARCH-in-mean (GARCHM[1,1]), MA-GARCHM(1,1), AR(1)-T-GARCHM(1,1), and ARMA(1,1)-TGARCHM( 1,1) outperform other models in terms of number of violations. ARMA(1,1)-T-GARCHM(1,1) performs the best in terms of mean violation range, mean violation percentage, aggregate violation range, aggregate violation percentage, and max violation range. Other than T-GARCH models, number of violations decrease by using in-mean or MA(1) mean equation. Generally speaking, the better the performance in terms of violation, the larger the capital requirement is needed.