A Realized Variance for the Whole Day Based on Intermittent High-Frequency Data

We consider the problem of deriving an empirical measure ofdaily integrated variance (IV) in the situation where high-frequencyprice data are unavailable for part of the day. We study threeestimators in this context and characterize the assumptionsthat justify their use. We show that the optimal combinationof the realized variance and squared overnight return can bedetermined, despite the latent nature of IV, and we discussthis result in relation to the problem of combining forecasts.Finally, we apply our theoretical results and construct fouryears of daily volatility estimates for the 30 stocks of theDow Jones Industrial Average.