In a country, the financial markets depend on several economic factors. One of these important factors is the export of the country. The stock index of the country tends to be raised due to the exports, though it may occur after some time rather than immediately. In this study, an attempt has been made to predict the best model of volatility in top export countries, Germany, China, the United States, Japan and Hong Kong by taking into account the closing price of the stock index of the sampled countries for a period ranging from the year 2000 to 2020. The returns from the stock markets are asymmetric; negative returns are found to be followed by a greater increase in volatility than the corresponding positive returns. Therefore, both symmetric and asymmetric generalised autoregressive conditional heteroscedasticity (GARCH) models have been applied to predict the volatility. The symmetric model used is GARCH (1,1) and asymmetric models used in the study are exponential GARCH (1,1) and GJR-GARCH (1,1). The study shows that EGARCH model has outperformed the GARCH and GJR-GARCH models in estimating the volatility in four stock indices ( Hanif & Pok, 2010 ; Kışınbay, 2010 ; Lin, 2018 ), and GJR-GARCH has outperformed in estimating volatility in one stock index ( Oberholzer & Venter, 2015 ; Shamiri & Hassan, 2007 ). The benefit of this study is to help portfolio managers, investors and corporations in making investment-related decisions. JEL Codes: C20, C31, C58, G12