A Fourier transform method for nonparametric estimation of multivariate volatility
Paul Malliavin, Maria Elvira Mancino
The Annals of Statistics · 2009 · Volume 37 · Issue 4
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.
Keywords
42A38, 60H10, 62F12, 62G05, 62P20, Continuous semi-martingale, Fourier transform, High frequency data, instantaneous co-volatility, nonparametric estimation
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