Fourier series method for measurement of multivariate volatilities

Maria Elvira Mancino and Paul Malliavin ()
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Paul Malliavin: 10 rue Saint Louis en l'Isle, 75004 Paris, France

Finance and Stochastics, 2002, vol. 6, issue 1, 49-61

Abstract: We present a methodology based on Fourier series analysis to compute time series volatility when the data are observations of a semimartingale. The procedure is not based on the Wiener theorem for the quadratic variation, but on the computation of the Fourier coefficients of the process and therefore it relies on the integration of the time series rather than on its differentiation. The method is fully model free and nonparametric. These features make the method well suited for financial market applications, and in particular for the analysis of high frequency time series and for the computation of cross volatilities.

Keywords: Volatility; Fourier series; financial time series (search for similar items in EconPapers)
JEL-codes: C14 C32 C63 (search for similar items in EconPapers)
Date: 2002-01-18
Note: received: October 2000; final version received: January 2001
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Citations: View citations in EconPapers (122)

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