We study the impact of oil price shocks on U.S. stock market volatility. We derive three different structural oil shock variables (i.e. aggregate demand, oil-supply, and oil-demand shocks) and relate them to stock market volatility, using bivariate structural VAR models, one for each oil price shock. Identification is achieved by assuming that the price of crude oil reacts to stock market volatility only with delay. This implies that innovations to the price of crude oil are not strictly exogenous, but predetermined with respect to the stock market. We show that volatility responds significantly to oil price shocks caused by sudden changes in aggregate and oil-specific demand, while the impact of supply-side shocks is negligible.