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

Published online by Cambridge University Press:  14 July 2016

Ole E. Barndorff-Nielsen ,
Svend Erik Graversen  and
Neil Shephard
Ole E. Barndorff-Nielsen
Affiliation:
Centre for Mathematical Physics and Stochastics (MaPhySto), University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Denmark. Email address: oebn@imf.au.dk
Svend Erik Graversen
Affiliation:
Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Denmark. Email address: matseg@imf.au.dk
Neil Shephard
Affiliation:
Nuffield College, University of Oxford, Oxford OX1 1NF, UK. Email address: neil.shephard@nuffield.oxford.ac.uk
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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.

Keywords

Bipowermixed Gaussian limitpower variationquadratic variationrealised variancerealised volatilitystochastic volatility
Type
Part 3. Financial mathematics
Information
Journal of Applied Probability , Volume 41 , Issue A: Stochastic Methods and their Applications , 2004 , pp. 133 - 143
Copyright
Copyright © Applied Probability Trust 2004 

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