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

  • Fukasawa, Masaaki
  • Rosenbaum, Mathieu
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    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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    File URL: http://www.sciencedirect.com/science/article/pii/S030441491200172X
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    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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    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. Silja Kinnebrock & Mark Podolskij, 2007. "A Note on the Central Limit Theorem for Bipower Variation of General Functions," OFRC Working Papers Series 2007fe03, Oxford Financial Research Centre.
    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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