Financial market volatility of developed economies have been studied extensively since the 1987 stock market crash as well as the volatility of the East Asian stock markets after the East Asian financial crisis. However the volatility characteristics of the financial markets in the Middle East are far from being thoroughly analysed despite their tremendous growth in recent years. The purpose of this paper is twofold. First, we investigate the volatility characteristics of the UAE stock markets measured by fat tail, volatility clustering, and leverage effects, in order to explore a parsimonious model for the UAE stock market and predict its future performance. Second, we use switching regime ARCH methodology to assess the impact of stock market openness to foreign investors on the market returns and we analyse its observed irregular performance using recently developed methodologies.