Nonparametric estimation of the volatility under microstructure noise: wavelet adaptation

Marc Hoffmann, Axel Munk and Johannes Schmidt-Hieber

MPRA Paper from University Library of Munich, Germany

Abstract: We study nonparametric estimation of the volatility function of a diffusion process from discrete data, when the data are blurred by additional noise. This noise can be white or correlated, and serves as a model for microstructure effects in financial modeling, when the data are given on an intra-day scale. By developing pre-averaging techniques combined with wavelet thresholding, we construct adaptive estimators that achieve a nearly optimal rate within a large scale of smoothness constraints of Besov type. Since the underlying signal (the volatility) is genuinely random, we propose a new criterion to assess the quality of estimation; we retrieve the usual minimax theory when this approach is restricted to deterministic volatility.

Keywords: Adaptive estimation; diffusion processes; high-frequency data; microstructure noise; minimax estimation; semimartingales; wavelets. (search for similar items in EconPapers)
JEL-codes: C0 C14 C22 (search for similar items in EconPapers)
Date: 2010-07-27
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-mst
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Citations: View citations in EconPapers (3)

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