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Large Deviations Of Realized Volatility

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Executive Summary

This paper studies large and moderate deviation properties of a realized volatility statistic of high frequency financial data. The authors establish a large deviation principle for the realized volatility when the number of high frequency observations in a fixed time interval increases to infinity. Their large deviation result can be used to evaluate tail probabilities of the realized volatility. They 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.

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