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Spectral characterization of the quadratic variation of mixed Brownian–fractional Brownian motion

  • Ehsan AzmoodehEmail author
  • Esko Valkeila
Article
  • 196 Downloads

Abstract

Dzhaparidze and Spreij (Stoch Process Appl, 54:165–174, 1994) showed that the quadratic variation of a semimartingale can be approximated using a randomized periodogram. We show that the same approximation is valid for a special class of continuous stochastic processes. This class contains both semimartingales and non-semimartingales. The motivation comes partially from the recent work by Bender et al. (Finance Stoch, 12:441–468, 2008), where it is shown that the quadratic variation of the log-returns determines the hedging strategy.

Keywords

Fractional Brownian motion Quadratic variation Randomized periodogram 

Mathematics Subject Classification

60G15 62M15 

Notes

Acknowledgments

Azmoodeh is grateful to Finnish Graduate School in Stochastic and Statistic (FGSS) for financial support, and Valkeila acknowledges the support of Academy of Finland, Grant 212875. We are grateful to an anonymous referee for a careful reading of the two versions of this paper.

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Mathematics and Systems AnalysisAalto University AaltoFinland

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