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

Masaaki Fukasawa and Mathieu Rosenbaum

Stochastic Processes and their Applications, 2012, vol. 122, issue 12, 3901-3920

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.

Keywords: Central limit theorem; Hitting times; Irregular grid; Semi-martingales; Stable convergence (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (11)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:122:y:2012:i:12:p:3901-3920

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DOI: 10.1016/j.spa.2012.08.005

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