In this paper we explore the relevance of asymmetry long memory and fat tails in modeling and forecasting the conditional volatility and market risk for the Gulf Cooperation Council (GCC) stock markets. Various linear and non-linear long-memory GARCH-class models under three density functions are used to investigate this relevancy. Our results reveal that non-linear GARCH-class models accommodating long memory and asymmetry can better capture the volatility of returns. In particular we find that some stock returns’ behaviors are well described by dual long memory in the mean and the conditional variances. Interestingly the FIAPARCH volatility model with skewed Student distribution is found to be the best suited for estimating the value at risk and expected shortfall for short and long trading positions. This model outperforms the other competing long-memory GARCH-class models and simple GARCH and EGARCH models. Overall long-memory asymmetry persistence and fat tails are important empirical facts in the GCC markets that should be taken into account when modeling and predicting volatility and assessing total risk. Our findings offer several useful implications for policy regulation risk assessment and hedging stock-price forecasting and portfolio asset allocations.