Large Deviations of Realized Volatility

Shin Kanaya and Taisuke Otsu
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Taisuke Otsu: Cowles Foundation, Yale University, https://cowles.yale.edu/

No 1798, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This 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.

Keywords: Realized volatility; Large deviation; Moderate deviation (search for similar items in EconPapers)
JEL-codes: C10 C20 C58 (search for similar items in EconPapers)
Pages: 37 pages
Date: 2011-05
New Economics Papers: this item is included in nep-ecm, nep-mst and nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Journal Article: Large deviations of realized volatility (2012)
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