Assessing the performance of generalized autoregressive conditional heteroskedasticity-based value-at-risk models: a case of frontier markets

ABSTRACT This paper assesses the performance of twelve generalized autoregressive conditional heteroskedasticity (GARCH)-type models for modeling the 99% value-at-risk (VaR) for indexes from countries classified as frontier economies, namely, Mauritius, Tunisia, Sri Lanka, Pakistan, Kazakhstan and Croatia. Leverage effects and long memory in volatility are considered by making use of exponential GARCH (EGARCH), Glosten-Jagannathan-Runkle (GJR) and integrated GARCH (IGARCH) models. The backtesting process is twofold, making use of recognized hypothesis tests for assessing coverage and loss functions for accuracy. Models are estimated using pre-financial crisis data and backtested over 500 days (within the 2008 crisis) of increased volatility. Despite returns exhibiting high kurtosis the assumption of normality for innovations in the GARCH models sometimes provides better VaR estimates. The standard GARCH also proves more useful than asymmetric models or the IGARCH in several cases. Results show that the EGARCH model generally overestimates VaR, except for Mauritius, with skewed t innovations. Following backtesting, we find that the Tunisian and Croatian indexes each have five models accepted, with two models in common. However, the Colombo index finds only the GARCH with normal innovations working satisfactorily. This study indicates that one model cannot be singled out for the indexes and that correct VaR estimation requires different model specifications for each market.