Hoffmann, Marc and Munk, Axel and SchmidtHieber, Johannes (2010): Nonparametric estimation of the volatility under microstructure noise: wavelet adaptation.

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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 intraday scale. By developing preaveraging 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.
Item Type:  MPRA Paper 

Original Title:  Nonparametric estimation of the volatility under microstructure noise: wavelet adaptation 
Language:  English 
Keywords:  Adaptive estimation; diffusion processes; highfrequency data; microstructure noise; minimax estimation; semimartingales; wavelets. 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C14  Semiparametric and Nonparametric Methods: General C  Mathematical and Quantitative Methods > C0  General C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes 
Item ID:  24562 
Depositing User:  Johannes SchmidtHieber 
Date Deposited:  22. Aug 2010 00:25 
Last Modified:  14. Mar 2015 12:46 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/24562 