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Central limit theorems for realized volatility under hitting times of an irregular grid

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  • Fukasawa, Masaaki
  • Rosenbaum, Mathieu
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    Abstract

    We consider a continuous semi-martingale sampled at hitting times of an irregular grid. The goal of this work is to analyze the asymptotic behavior of the realized volatility under this rather natural observation scheme. This framework strongly differs from the well understood situations when the sampling times are deterministic or when the grid is regular. Indeed, neither Gaussian approximations nor symmetry properties can be used. In this setting, as the distance between two consecutive barriers tends to zero, we establish central limit theorems for the normalized error of the realized volatility. In particular, we show that there is no bias in the limiting process.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 122 (2012)
    Issue (Month): 12 ()
    Pages: 3901-3920

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    Handle: RePEc:eee:spapps:v:122:y:2012:i:12:p:3901-3920

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    Related research

    Keywords: Central limit theorem; Hitting times; Irregular grid; Semi-martingales; Stable convergence;

    References

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    1. Masaaki Fukasawa, 2010. "Central limit theorem for the realized volatility based on tick time sampling," Finance and Stochastics, Springer, vol. 14(2), pages 209-233, April.
    2. Kinnebrock, Silja & Podolskij, Mark, 2008. "A note on the central limit theorem for bipower variation of general functions," Stochastic Processes and their Applications, Elsevier, vol. 118(6), pages 1056-1070, June.
    3. Fukasawa, Masaaki, 2010. "Realized volatility with stochastic sampling," Stochastic Processes and their Applications, Elsevier, vol. 120(6), pages 829-852, June.
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    Cited by:
    1. Li, Yingying & Zhang, Zhiyuan & Zheng, Xinghua, 2013. "Volatility inference in the presence of both endogenous time and microstructure noise," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2696-2727.
    2. Markus Bibinger & Mathias Vetter, 2013. "Estimating the quadratic covariation of an asynchronously observed semimartingale with jumps," SFB 649 Discussion Papers SFB649DP2013-029, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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