Large Deviations of Realized Volatility
AbstractThis paper studies large and moderate deviation properties of a realized volatility statistic of high frequency financial data. We establish a large deviation principle for the realized volatility when the number of high frequency observations in a fixed time interval increases to infinity. Our large deviation result can be used to evaluate tail probabilities of the realized volatility. We also derive a moderate deviation rate function for a standardized realized volatility statistic. The moderate deviation result is useful for assessing the validity of normal approximations based on the central limit theorem. In particular, it clarifies that there exists a trade-off between the accuracy of the normal approximations and the path regularity of an underlying volatility process. Our large and moderate deviation results complement the existing asymptotic theory on high frequency data. In addition, the paper contributes to the literature of large deviation theory in that the theory is extended to a high frequency data environment.
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Bibliographic InfoPaper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1798.
Length: 37 pages
Date of creation: May 2011
Date of revision:
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
Other versions of this item:
- C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
- C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
- C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-05-14 (All new papers)
- NEP-ECM-2011-05-14 (Econometrics)
- NEP-MST-2011-05-14 (Market Microstructure)
- NEP-RMG-2011-05-14 (Risk Management)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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"A central limit theorem for realised power and bipower variations of continuous semimartingales,"
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OFRC Working Papers Series
2005fe09, Oxford Financial Research Centre.
- Barndorff-Nielsen, Ole E. & Graversen, Svend Erik & Jacod, Jean & Shephard, Neil, 2006. "Limit Theorems For Bipower Variation In Financial Econometrics," Econometric Theory, Cambridge University Press, vol. 22(04), pages 677-719, August.
- Ole E. Barndorff-Nielsen & Sven Erik Graversen & Jean Jacod & Neil Shephard, 2005. "Limit theorems for bipower variation in financial econometrics," Economics Papers 2005-W06, Economics Group, Nuffield College, University of Oxford.
- repec:oxf:wpaper:264 is not listed on IDEAS
- Meddahi, Nour & Mykland, Per & Shephard, Neil, 2011. "Realized Volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 1-1, January.
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