Primary aim of this research is to contribute to the literature on oil prices and stock markets by studying the relation between oil price volatility and stock market volatility. We use a large sample of developed and emerging stock market indices, based on monthly observations over the period January 1982 – December 2008. Volatility is approximated as realized volatility and our methodology is based on regression analysis. Results indicate that one month lagged oil price volatility has significant predicting power in a considerable number of stock market indices, despite the high persistence of stock market volatility. The explanatory power of our model is maximized with the inclusion of an additional lag of five or ten days, which is consistent with the existence of delayed reaction by investors. Furthermore, sector analysis reveals that oil price volatility has greater influence in non oil related industries than in oil related. Additionally, we find strong evidence of asymmetric effects of oil prices on stock market returns. The results denote that increases on oil price appear to have a larger (and negative) impact on the stock market indices than the decreases. Moreover, the existence of asymmetric effects on oil price volatility to stock market volatility is not supported by empirical evidence.