Large deviations of realized volatility

Shin Kanaya, Taisuke Otsu

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 languageEnglish
Pages (from-to)546-581
Number of pages36
JournalStochastic Processes and their Applications
Volume122
Issue number2
DOIs
Publication statusPublished - 2012 Jan 1
Externally publishedYes

Fingerprint

Realized Volatility
Moderate Deviations
Large Deviations
High-frequency Data
Statistics
Normal Approximation
Statistic
Large Deviation Theory
Tail Probability
Financial Data
Large Deviation Principle
Rate Function
Asymptotic Theory
Central limit theorem
Volatility
Complement
Trade-offs
Regularity
Infinity
Path

Keywords

  • Large deviation
  • Moderate deviation
  • Realized volatility

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

Cite this

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

In: Stochastic Processes and their Applications, Vol. 122, No. 2, 01.01.2012, p. 546-581.

Research output: Contribution to journalArticle

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