CFDP 1798

Large Deviations of Realized Volatility

Author(s): 

Publication Date: May 2011

Pages: 37

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

JEL Classification Codes:  C10, C20, C58

Note: 

Published in Stochastic Processes and Their Applications (February 2012), 122(2): 546-581 [DOI]