A Fourier transform method for nonparametric estimation of multivariate volatility

By Paul Malliavin, Maria Elvira Mancino. 2009

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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.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/49ea485b7abd39cc800b9a6d309a43fcc20f381e