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Rounding Errors and Volatility Estimation.

Financial prices are often discretized--with smallest tick size of one cent, for example. Thus prices involve rounding errors. Rounding errors affect the estimation of volatility, and understanding them is critical, particularly when using high frequency data. We study the asymptotic behavior of rea...

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Published in:Journal of Financial Econometrics Vol. 13; no. 2; pp. 478 - 505
Main Authors: YINGYING LI, MYKLAND, PER A.
Format: Article
Published: Oxford University Press / USA Spring2015
Subjects:
Market volatility
Estimation theory
Rounding errors
Stochastic convergence
Statistical bias
Online Access:View this record in EBSCOhost
Summary:Financial prices are often discretized--with smallest tick size of one cent, for example. Thus prices involve rounding errors. Rounding errors affect the estimation of volatility, and understanding them is critical, particularly when using high frequency data. We study the asymptotic behavior of realized volatility (RV), which is commonly used as an estimator of integrated volatility. We prove the convergence of the RV and scaled RV under varous conditions on the rounding level and the number of observations. A bias-corrected volatility estimator is proposed and an associated central limit theorem is shown. The simulation and empirical results demonstrate that the proposed method can yield substantial statistical improvement.