Volatility analysis for the GARCH-Itô model with option data

Low-frequency historical data, high-frequency historical data, and option data are three primary sources that can be used to forecast an underlying security's volatility. In this article, we propose an explicit model integrating the three information sources. Instead of directly using option price data, we extract option-implied volatility from option data and estimate its dynamics. We provide joint quasimaximum likelihood estimators for the parameters and establish their asymptotic properties. Real data examples demonstrate that the proposed model has better out-of-sample volatility forecasting performance than other popular volatility models.