  Volatility asymmetry is a hot topic in high-frequency financial market. In
this paper, we propose a new econometric model, which could describe volatility
asymmetry based on high-frequency historical data and low-frequency historical
data. After providing the quasi-maximum likelihood estimators for the
parameters, we establish their asymptotic properties. We also conduct a series
of simulation studies to check the finite sample performance and volatility
forecasting performance of the proposed methodologies. And an empirical
application is demonstrated that the new model has stronger volatility
prediction power than GARCH-It\^{o} model in the literature.
