This paper investigates estimation of extreme risk in a number of stock markets in the Gulf Cooperation Council (GCC) countries(1), Saudi, Kuwait, and United Arab Emirates, in addition to S& P 500 stock index, using the Generalized Pareto Distribution (GPD) model. The estimated tails parameter values for stock returns of Kuwait, Saudi, and Dubai, markets show the likelihood of significant extreme losses as well as significant extreme gains, compared to the case of more mature S&P 500 stock returns, which exhibit possibility of significant extreme losses with insignificant gain prospects.