  Low-frequency historical data, high-frequency historical data and option data
are three major sources, which can be used to forecast the underlying
security's volatility. In this paper, we propose two econometric models, which
integrate three information sources. In GARCH-It\^{o}-OI model, we assume that
the option-implied volatility can influence the security's future volatility,
and the option-implied volatility is treated as an observable exogenous
variable. In GARCH-It\^{o}-IV model, we assume that the option-implied
volatility can not influence the security's volatility directly, and the
relationship between the option-implied volatility and the security's
volatility is constructed to extract useful information of the underlying
security. After providing the quasi-maximum likelihood estimators for the
parameters and establishing their asymptotic properties, we also conduct a
series of simulation analysis and empirical analysis to compare the proposed
models with other popular models in the literature. We find that when the
sampling interval of the high-frequency data is 5 minutes, the GARCH-It\^{o}-OI
model and GARCH-It\^{o}-IV model has better forecasting performance than other
models.
