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Fourier series method for measurement of multivariate volatilities

Author

Listed:
  • Maria Elvira Mancino

    () (DIMAD, Università di Firenze, Via C.Lombroso 6/17, 50134 Firenze, Italy Manuscript)

  • Paul Malliavin

    () (10 rue Saint Louis en l'Isle, 75004 Paris, France)

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.

Suggested Citation

  • Maria Elvira Mancino & Paul Malliavin, 2002. "Fourier series method for measurement of multivariate volatilities," Finance and Stochastics, Springer, vol. 6(1), pages 49-61.
  • Handle: RePEc:spr:finsto:v:6:y:2002:i:1:p:49-61
    Note: received: October 2000; final version received: January 2001
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    Keywords

    Volatility; Fourier series; financial time series;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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