Journal Article

Microstructure Noise, Realized Variance, and Optimal Sampling

F. M. Bandi and J. R. Russell

in The Review of Economic Studies

Published on behalf of Review of Economic Studies Ltd

Volume 75, issue 2, pages 339-369
Published in print April 2008 | ISSN: 0034-6527
Published online April 2008 | e-ISSN: 1467-937X | DOI: http://dx.doi.org/10.1111/j.1467-937X.2008.00474.x
Microstructure Noise, Realized Variance, and Optimal Sampling

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A recent and extensive literature has pioneered the summing of squared observed intra-daily returns, “realized variance”, to estimate the daily integrated variance of financial asset prices, a traditional object of economic interest. We show that, in the presence of market microstructure noise, realized variance does not identify the daily integrated variance of the frictionless equilibrium price. However, we demonstrate that the noise-induced bias at very high sampling frequencies can be appropriately traded off with the variance reduction obtained by high-frequency sampling and derive a mean-squared-error (MSE) optimal sampling theory for the purpose of integrated variance estimation. We show how our theory naturally leads to an identification procedure, which allows us to recover the moments of the unobserved noise; this procedure may be useful in other applications. Finally, using the profits obtained by option traders on the basis of alternative variance forecasts as our economic metric, we find that explicit optimization of realized variance's finite sample MSE properties results in accurate forecasts and considerable economic gains.

Keywords: G12; G13

Journal Article.  12430 words.  Illustrated.

Subjects: Economics

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