Power variation and stochastic volatility: a review and some new results

Power variation and stochastic volatility: a review and some new results

Ole E. Barndorff-Nielsen, Svend Erik Graversen, and Neil Shephard

Source: J. Appl. Probab. Volume 41A, Issue (2004), 133-143.

Abstract

In this paper we review some recent work on limit results on realised power variation, that is, sums of powers of absolute increments of various semimartingales. A special case of this analysis is realised variance and its probability limit, quadratic variation. Such quantities often appear in financial econometrics in the analysis of volatility. The paper also provides some new results and discusses open issues.

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Primary Subjects: 60-XX

Secondary Subjects: 91Bxx

Keywords: Bipower; mixed Gaussian limit; power variation; quadratic variation; realised variance; realised volatility; stochastic volatility

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Permanent link to this document: http://projecteuclid.org/euclid.jap/1082552195
Digital Object Identifier: doi:10.1239/jap/1082552195
Mathematical Reviews number (MathSciNet): MR2057570
Zentralblatt MATH identifier: 02109916

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