### 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.

Original language | English |
---|---|

Pages (from-to) | 546-581 |

Number of pages | 36 |

Journal | Stochastic Processes and their Applications |

Volume | 122 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2012 Jan 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Large deviation
- Moderate deviation
- Realized volatility

### ASJC Scopus subject areas

- Statistics and Probability
- Modelling and Simulation
- Applied Mathematics

### Cite this

*Stochastic Processes and their Applications*,

*122*(2), 546-581. https://doi.org/10.1016/j.spa.2011.09.002

**Large deviations of realized volatility.** / Kanaya, Shin; Otsu, Taisuke.

Research output: Contribution to journal › Article

*Stochastic Processes and their Applications*, vol. 122, no. 2, pp. 546-581. https://doi.org/10.1016/j.spa.2011.09.002

}

TY - JOUR

T1 - Large deviations of realized volatility

AU - Kanaya, Shin

AU - Otsu, Taisuke

PY - 2012/1/1

Y1 - 2012/1/1

N2 - 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.

AB - 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.

KW - Large deviation

KW - Moderate deviation

KW - Realized volatility

UR - http://www.scopus.com/inward/record.url?scp=84155167123&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84155167123&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2011.09.002

DO - 10.1016/j.spa.2011.09.002

M3 - Article

AN - SCOPUS:84155167123

VL - 122

SP - 546

EP - 581

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

IS - 2

ER -