A tale of two time scales: Determining integrated volatility with noisy high-frequency data

Lan Zhang, Per A. Mykland, Yacine Aït-Sahalia

Research output: Contribution to journalArticle

791 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1394-1411
Number of pages18
JournalJournal of the American Statistical Association
Volume100
Issue number472
DOIs
StatePublished - Dec 1 2005

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Bias-correction
  • Market microstructure
  • Martingale
  • Measurement error
  • Realized volatility
  • Subsampling

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