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Functional Principal Component Analysis for Derivatives of Multivariate Curves

Author

Listed:
  • Maria Grith
  • Wolfgang K. Härdle
  • Alois Kneip
  • Heiko Wagner

Abstract

We present two methods based on functional principal component analysis (FPCA) for the estimation of smooth derivatives of a sample of random functions, which are observed in a more than one-dimensional domain. We apply eigenvalue decomposition to a) the dual covariance matrix of the derivatives, and b) the dual covariance matrix of the observed curves. To handle noisy data from discrete observations, we rely on local polynomial regressions. If curves are contained in a finite-dimensional function space, the second method performs better asymptotically. We apply our methodology in a simulation and empirical study, in which we estimate state price density (SPD) surfaces from call option prices. We identify three main components, which can be interpreted as volatility, skewness and tail factors. We also find evidence for term structure variation.

Suggested Citation

  • Maria Grith & Wolfgang K. Härdle & Alois Kneip & Heiko Wagner, 2016. "Functional Principal Component Analysis for Derivatives of Multivariate Curves," SFB 649 Discussion Papers SFB649DP2016-033, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2016-033
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    References listed on IDEAS

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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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