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The Dynamics of Implied Volatilities: A Common Principal Components Approach

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  • Matthias Fengler

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  • Wolfgang Härdle
  • Christophe Villa

Abstract

It is common practice to identify the number and sources of shocks that move, e.g., ATM implied volatilities by principal components analysis. This approach, however, is likely to result in a loss of information, since the surface structure of implied volatilities is neglected. In this paper we analyze the implied volatility surface along maturity slices with a common principal components analysis (CPC), known from morphometrics. In CPC analysis, the space spanned by the eigenvectors is identical across groups, whereas variances associated with the common principal components vary. Our analysis shows that implied volatility surface dynamics can be traced back to a common eigenstructure in maturity slices. This empirical result is used to set up a factor model for implied volatility surface dynamics. Copyright Kluwer Academic Publishers 2003

Suggested Citation

  • Matthias Fengler & Wolfgang Härdle & Christophe Villa, 2003. "The Dynamics of Implied Volatilities: A Common Principal Components Approach," Review of Derivatives Research, Springer, vol. 6(3), pages 179-202, October.
  • Handle: RePEc:kap:revdev:v:6:y:2003:i:3:p:179-202
    DOI: 10.1023/B:REDR.0000004823.77464.2d
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    References listed on IDEAS

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    1. Fengler, Matthias R. & Härdle, Wolfgang & Mammen, Enno, 2003. "Implied volatility string dynamics," SFB 373 Discussion Papers 2003,54, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
    3. Farshid Jamshidian & Yu Zhu, 1996. "Scenario Simulation: Theory and methodology (*)," Finance and Stochastics, Springer, vol. 1(1), pages 43-67.
    4. Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1998. "Implied Volatility Functions: Empirical Tests," Journal of Finance, American Finance Association, vol. 53(6), pages 2059-2106, December.
    5. Fengler, Matthias R. & Wang, Qihua, 2003. "Fitting the Smile Revisited: A Least Squares Kernel Estimator for the Implied Volatility Surface," SFB 373 Discussion Papers 2003,25, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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    More about this item

    Keywords

    common principal component analysis; principal component analysis; factor model; implied volatility surface; smile;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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