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

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Abstract
We consider the problem of deriving an empirical measure of daily integrated variance (IV) in the situation where high-frequency price data are unavailable for part of the day. We study three estimators in this context and characterize the assumptions that justify their use. We show that the optimal combination of the realized variance and squared overnight return can be determined, despite the latent nature of IV, and we discuss this result in relation to the problem of combining forecasts. Finally, we apply our theoretical results and construct four years of daily volatility estimates for the 30 stocks of the Dow Jones Industrial Average.

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