Modeling Volatility Using High Frequency Data

This dissertation explores the volatility of stock prices over the course of a trading day. I reformulate the Heston stochastic volatility model as a model of the high-frequency evolution of the scaled increments of quadratic variation. I use the generalized method of moments to estimate three of the parameters of the model: the speed of mean reversion, the asymptotic mean, and the volatility of volatility. This continuous-path model works very well most of the time, and most of the failures are localized to a few short intervals