Finance and Stochastics

, Volume 6, Issue 1, pp 49–61 | Cite as

Fourier series method for measurement of multivariate volatilities

  • Paul Malliavin
  • Maria Elvira Mancino
Original Paper


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.

Key words: Volatility, Fourier series, financial time series 
JEL Classification: C14, C32, C63 
Mathematics Subject Classification (1991): 42B05, 62H12, 62M15, 62P20 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Paul Malliavin
    • 1
  • Maria Elvira Mancino
    • 2
  1. 1.10 rue Saint Louis en l'Isle, 75004 Paris, France (e-mail: FR
  2. 2.DIMAD, Università di Firenze, Via C.Lombroso 6/17, 50134 Firenze, Italy (e-mail: IT

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