Estimation of Stock Price Variances and Serial Covariances from Discrete Observations

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Abstract
Stock price discreteness adds noise to price series. The noise increases return variances and adds negative serial correlation to return series. Standard variance and serial covariance estimators therefore overestimate the variance and serial covariance of the underlying stock values. Discreteness-induced variance and serial covariance depend on underlying volatility and on the size of the bid/ask spread. Simple formulas for approximating the effects of discreteness on variance and serial correlation are derived and presented. The approximations, which are accurate in daily data, can be used to adjust the standard variance and serial covariance estimators.

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