Spectral Estimation of Covolatility from Noisy Observations Using Local Weights

Markus Bibinger and Markus Reiß

Scandinavian Journal of Statistics, 2014, vol. 41, issue 1, 23-50

Abstract: type="main" xml:id="sjos12019-abs-0001"> We propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes, which are observed discretely with additive observation noise. The appropriate estimation for time-varying volatilities is based on an asymptotic equivalence of the underlying statistical model to a white-noise model with correlation and volatility processes being constant over small time intervals. The asymptotic equivalence of the continuous-time and discrete-time experiments is proved by a construction with linear interpolation in one direction and local means for the other. The new estimator outperforms earlier non-parametric methods in the literature for the considered model. We investigate its finite sample size characteristics in simulations and draw a comparison between various proposed methods.

Date: 2014
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