Central limit theorems for realized volatility under hitting times of an irregular grid |
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Authors: | Masaaki Fukasawa Mathieu Rosenbaum |
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Institution: | 1. Department of Mathematics, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka, Japan;2. Laboratoire de Probabilités et Modèles Aléatoires, Université Pierre et Marie Curie (Paris-6), 4 Place Jussieu, 75252 Paris Cedex 05, France |
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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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Keywords: | 60F05 60F17 60G40 60G44 62M99 |
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