A Fourier transform method for nonparametric estimation of multivariate volatility
Abstract
We provide a nonparametric method for the computation of instantaneous multivariate volatility for continuous semi-martingales, which is based on Fourier analysis. The co-volatility is reconstructed as a stochastic function of time by establishing a connection between the Fourier transform of the prices process and the Fourier transform of the co-volatility process. A nonparametric estimator is derived given a discrete unevenly spaced and asynchronously sampled observations of the asset price processes. The asymptotic properties of the random estimator are studied: namely, consistency in probability uniformly in time and convergence in law to a mixture of Gaussian distributions.
Cite
@article{arxiv.0908.1890,
title = {A Fourier transform method for nonparametric estimation of multivariate volatility},
author = {Paul Malliavin and Maria Elvira Mancino},
journal= {arXiv preprint arXiv:0908.1890},
year = {2009}
}
Comments
Published in at http://dx.doi.org/10.1214/08-AOS633 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)