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Low-frequency historical data, high-frequency historical data and option dataare three major sources, which can be used to forecast the underlyingsecurity's volatility. In this paper, we propose two econometric models, whichintegrate three information sources. In GARCH-It\^{o}-OI model, we assume thatthe option-implied volatility can influence the security's future volatility,and the option-implied volatility is treated as an observable exogenousvariable. In GARCH-It\^{o}-IV model, we assume that the option-impliedvolatility can not influence the security's volatility directly, and therelationship between the option-implied volatility and the security'svolatility is constructed to extract useful information of the underlyingsecurity. After providing the quasi-maximum likelihood estimators for theparameters and establishing their asymptotic properties, we also conduct aseries of simulation analysis and empirical analysis to compare the proposedmodels with other popular models in the literature. We find that when thesampling interval of the high-frequency data is 5 minutes, the GARCH-It\^{o}-OImodel and GARCH-It\^{o}-IV model has better forecasting performance than othermodels.

Forecasting security's volatility using low-frequency historical data, high-frequency historical data and option-implied volatility