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A Tale of Two Time Scales

A Tale of Two Time Scales It is a common practice in finance to estimate volatility from the sum of frequently sampled squared returns. However, market microstructure poses challenges to this estimation approach, as evidenced by recent empirical studies in finance. The present work attempts to lay out theoretical grounds that reconcile continuous-time modeling and discrete-time samples. We propose an estimation approach that takes advantage of the rich sources in tick-by-tick data while preserving the continuous-time assumption on the underlying returns. Under our framework, it becomes clear why and where the “usual” volatility estimator fails when the returns are sampled at the highest frequencies. If the noise is asymptotically small, our work provides a way of finding the optimal sampling frequency. A better approach, the “two-scales estimator,” works for any size of the noise. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the American Statistical Association Taylor & Francis

A Tale of Two Time Scales

18 pages

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References (30)

Publisher
Taylor & Francis
Copyright
© American Statistical Association
ISSN
1537-274X
eISSN
0162-1459
DOI
10.1198/016214505000000169
Publisher site
See Article on Publisher Site

Abstract

It is a common practice in finance to estimate volatility from the sum of frequently sampled squared returns. However, market microstructure poses challenges to this estimation approach, as evidenced by recent empirical studies in finance. The present work attempts to lay out theoretical grounds that reconcile continuous-time modeling and discrete-time samples. We propose an estimation approach that takes advantage of the rich sources in tick-by-tick data while preserving the continuous-time assumption on the underlying returns. Under our framework, it becomes clear why and where the “usual” volatility estimator fails when the returns are sampled at the highest frequencies. If the noise is asymptotically small, our work provides a way of finding the optimal sampling frequency. A better approach, the “two-scales estimator,” works for any size of the noise.

Journal

Journal of the American Statistical AssociationTaylor & Francis

Published: Dec 1, 2005

Keywords: Bias-correction; Market microstructure; Martingale; Measurement error; Realized volatility; Subsampling

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