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arXiv · 0908.1890

A Fourier transform method for nonparametric estimation of multivariate volatility

Paul Malliavin·Maria Elvira Mancino
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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.

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Paul Malliavin, Maria Elvira Mancino. 2009-08-13. A Fourier transform method for nonparametric estimation of multivariate volatility. https://doi.org/10.1214/08-aos633

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