## 抄録

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.

本文言語 | English |
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ページ（範囲） | 546-581 |

ページ数 | 36 |

ジャーナル | Stochastic Processes and their Applications |

巻 | 122 |

号 | 2 |

DOI | |

出版ステータス | Published - 2012 2 |

外部発表 | はい |

## ASJC Scopus subject areas

- 統計学および確率
- モデリングとシミュレーション
- 応用数学