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Principal Components Analysis in implied volatility modeling (Analiza skladowych glownych w modelowaniu implikowanej zmiennosci)

Author

Listed:
  • Rafal Weron
  • Slawomir Wojcik

Abstract

We analyze the implied volatility surface structure of ODAX options as traded on DTB (currently Eurex). We apply PCA to cross sections of the implied volatility surface taken along the same moneyness (m) or the same time to maturity (T). For data from the period October 3rd 1997 – November 30th 1998 a substantial reduction of the dimensionality of the problem was achieved. It turned out that (i) for the m-sections the first two principal components contained 99.997% of information, and (ii) for the T-sections the first three principal components contained 99.892% of information. Moreover, the obtained principal components were very similar for different m's or T's allowing us to assume that that the space spanned by the eigenvectors is identical across several groups (of m's or T's), i.e. leading us to the so called Common PCA.

Suggested Citation

  • Rafal Weron & Slawomir Wojcik, 2004. "Principal Components Analysis in implied volatility modeling (Analiza skladowych glownych w modelowaniu implikowanej zmiennosci)," HSC Research Reports HSC/04/03, Hugo Steinhaus Center, Wroclaw University of Technology.
  • Handle: RePEc:wuu:wpaper:hsc0403
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    File URL: http://www.im.pwr.wroc.pl/~hugo/RePEc/wuu/wpaper/HSC_04_03.pdf
    File Function: Final version, 2004 (in Polish)
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    More about this item

    Keywords

    Volatility surface; ODAX option; Principal Component Analysis; Common PCA;

    JEL classification:

    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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