Forecasting value-at-risk for frontier stock market indexes using GARCH-type models and extreme value theory: model validation for dynamic models

ABSTRACT We discuss the relative performances of value-at-risk (VaR) models using generalized autoregressive conditional heteroscedasticity (GARCH), Glosten-Jagannathan-Runkle GARCH and integrated GARCH (IGARCH) for volatility forecasting, and extreme value theory (EVT) for approximating the fat tails of the standardized residuals. For the volatility estimation with two underlying distributions(normal and skewed t), we find that this affects the forecasted VaR figures in most cases. The peak over threshold method is used for estimating the tail of losses of the standardized residuals. The models obtained are applied to six frontier market indexes and backtested/validated using hypothesis tests and loss functions. We observe that the dynamic EVT models generally perform well, except for the Sri Lankan index, for which no model could be identified. Finally, we find that a dynamic EVT with an IGARCH volatility specification works well for four out of the six indexes considered, which may indicate that this model may suit other indexes from other frontier markets. We thus find that a mixed approach to VaR estimation using volatility models and EVT provides an appropriate framework for effectively estimating market risk.