COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1798 Large Deviations of Realized Volatility Shin Kanaya and Taisuke Otsu 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. |
