A central limit theorem for the functional estimation of the spot volatility

Ngo Hoang-Long and Ogawa Shigeyoshi
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Ngo Hoang-Long: Department of Mathematical Sciences, Ritsumeikan University, Shiga, Japan. Email: gr041086@ed.ritsumei.ac.jp
Ogawa Shigeyoshi: Department of Mathematical Sciences, Ritsumeikan University, Shiga, Japan. Email: ogawa-s@se.ritsumei.ac.jp

Monte Carlo Methods and Applications, 2009, vol. 15, issue 4, 353-380

Abstract: In this paper we introduce a class of statistics for the functional estimation of the spot volatility in the setting of frequency observed diffusion processes which may be disturbed by microstructure noise. We show that the limit theorems for the estimation of the spot volatility and the cross spot volatility of the statistics are still valid even if we add jump processes of finite or infinite activity to the underlying diffusion process. These statistics extend the quadratic variational approach and are related to the concept of multipower variation, which is used in the problem of estimating the integrated volatility.

Keywords: Spot volatility; central limit theorem; robustness; jump process; microstructure noise (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (2)

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DOI: 10.1515/MCMA.2009.019

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