In this study, we have investigated GCC stock market volatilities exploiting a number of asymmetric models (EGARCH, ICSS-EGARCH, GJR-GARCH, and ICSS-GJR-GARCH).This paper uses the weekly data over the period 2003-2010. The ICSS-EGARCH and ICSS-GJR-GARCH models take into account the discrete regime shifts in stochastic errors. The finding supports the widely accepted view that accounting for the regime shifts detected by the iterated cumulative sums of squares (ICSS) algorithm in the variance equations overcomes the overestimation of volatility persistence. In addition, we have discovered that the sudden changes are generally associated with global, regional, and domestic economic as well as political events. Importantly, the asymmetric model estimations use normal as well as heavy-tailed conditional densities.