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.
Publié le : 2009-08-15
Classification:
Continuous semi-martingale,
instantaneous co-volatility,
nonparametric estimation,
Fourier transform,
high frequency data,
62G05,
62F12,
42A38,
60H10,
62P20
@article{1245332838,
author = {Malliavin, Paul and Mancino, Maria Elvira},
title = {A Fourier transform method for nonparametric estimation of multivariate volatility},
journal = {Ann. Statist.},
volume = {37},
number = {1},
year = {2009},
pages = { 1983-2010},
language = {en},
url = {http://dml.mathdoc.fr/item/1245332838}
}
Malliavin, Paul; Mancino, Maria Elvira. A Fourier transform method for nonparametric estimation of multivariate volatility. Ann. Statist., Tome 37 (2009) no. 1, pp. 1983-2010. http://gdmltest.u-ga.fr/item/1245332838/