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

Overnight GARCH-It\^o Volatility Models