  Various parametric volatility models for financial data have been developed
to incorporate high-frequency realized volatilities and better capture market
dynamics. However, because high-frequency trading data are not available during
the close-to-open period, the volatility models often ignore volatility
information over the close-to-open period and thus may suffer from loss of
important information relevant to market dynamics. In this paper, to account
for whole-day market dynamics, we propose an overnight volatility model based
on It\^o diffusions to accommodate two different instantaneous volatility
processes for the open-to-close and close-to-open periods. We develop a
weighted least squares method to estimate model parameters for two different
periods and investigate its asymptotic properties. We conduct a simulation
study to check the finite sample performance of the proposed model and method.
Finally, we apply the proposed approaches to real trading data.
