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Large Deviations of Realized Volatility

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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.

Suggested Citation

  • Shin Kanaya & Taisuke Otsu, 2011. "Large Deviations of Realized Volatility," Cowles Foundation Discussion Papers 1798, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1798
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Hacène Djellout & Hui Jiang, 2018. "Large Deviations Of The Threshold Estimator Of Integrated (Co-)Volatility Vector In The Presence Of Jumps," Post-Print hal-01147189, HAL.
    2. Djellout, Hacène & Samoura, Yacouba, 2014. "Large and moderate deviations of realized covolatility," Statistics & Probability Letters, Elsevier, vol. 86(C), pages 30-37.
    3. Hacène Djellout & Hui Jiang, 2018. "Large Deviations of the Threshold Estimator of Integrated (Co-)Volatility Vector in the Presence of Jumps," Journal of Theoretical Probability, Springer, vol. 31(3), pages 1606-1624, September.
    4. Xinwei Feng & Lidan He & Zhi Liu, 2022. "Large Deviation Principles of Realized Laplace Transform of Volatility," Journal of Theoretical Probability, Springer, vol. 35(1), pages 186-208, March.
    5. Hacène Djellout & Hui Jiang, 2015. "Large Deviations Of The Threshold Estimator Of Integrated (Co-)Volatility Vector In The Presence Of Jumps," Working Papers hal-01147189, HAL.
    6. Hacène Djellout & Arnaud Guillin & Yacouba Samoura, 2014. "Large Deviations Of The Realized (Co-)Volatility Vector," Working Papers hal-01082903, HAL.
    7. Djellout, Hacène & Guillin, Arnaud & Samoura, Yacouba, 2017. "Estimation of the realized (co-)volatility vector: Large deviations approach," Stochastic Processes and their Applications, Elsevier, vol. 127(9), pages 2926-2960.
    8. Hacène Djellout & Arnaud Guillin & Yacouba Samoura, 2017. "Large Deviations Of The Realized (Co-)Volatility Vector," Post-Print hal-01082903, HAL.

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    More about this item

    Keywords

    Realized volatility; Large deviation; Moderate deviation;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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