This paper makes use of the distributional information contained in high-frequency data to test for the specification of the functional form of the volatility process within the class of stochastic volatility models. Itō’s calculus is implemented in order to obtain the first and second conditional moment of the driving stochastic differential equation for the volatility process. These analytical expressions are augmented by their lag and lag squared and are used to form the corresponding GMM estimator. The base case stochastic volatility model is extended to allow for the leverage effect and jumps in returns. Empirical estimation confirms the presence of fast mean reversion in volatility and jumps in returns for the 5-min S&P 500 stock market index. Further estimation results also seem to indicate the presence of jumps in the volatility process that are correlated to the jumps in returns.
