Publication Date: May 2011
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.
Realized volatility, Large deviation, Moderate deviation
JEL Classification Codes: C10, C20, C58
Published in Stochastic Processes and Their Applications (February 2012), 122(2): 546-581 [DOI]