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The Dynamics of Implied Volatilities: A Common Principal Components Approach

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  • Matthias Fengler

    ()

  • 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

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Bibliographic Info

Article provided by Springer in its journal Review of Derivatives Research.

Volume (Year): 6 (2003)
Issue (Month): 3 (October)
Pages: 179-202

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Handle: RePEc:kap:revdev:v:6:y:2003:i:3:p:179-202

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Web page: http://www.springerlink.com/link.asp?id=102989

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

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References

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  1. 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.
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Cited by:
  1. Wallmeier, Martin, 2012. "Smile in Motion: An Intraday Analysis of Asymmetric Implied Volatility," FSES Working Papers 427, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
  2. Ci­zek, P. & Tamine, J. & Härdle, W., 2008. "Smoothed L-estimation of regression function," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5154-5162, August.
  3. Fengler, Matthias & Hin, Lin-Yee, 2011. "Semi-nonparametric estimation of the call price surface under strike and time-to-expiry no-arbitrage constraints," Economics Working Paper Series 1136, University of St. Gallen, School of Economics and Political Science, revised May 2013.
  4. 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.
  5. Alejandro Bernales & Massimo Guidolin, 2012. "Can We Forecast the Implied Volatility Surface Dynamics of Equity Options? Predictability and Economic Value Tests," Working Papers 456, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  6. Bernd Engelmann & Matthias Fengler & Morten Nalholm & Peter Schwendner, 2006. "Static versus dynamic hedges: an empirical comparison for barrier options," Review of Derivatives Research, Springer, vol. 9(3), pages 239-264, November.
  7. Michal Benko & Alois Kneip, 2005. "Common functional component modelling," SFB 649 Discussion Papers SFB649DP2005-016, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  8. Pavel Cizek & Karel Komorad, 2005. "Implied Trinomial Trees," SFB 649 Discussion Papers SFB649DP2005-007, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  9. Ralf Brüggemann & Wolfgang Härdle & Julius Mungo & Carsten Trenkler, 2006. "VAR Modeling for Dynamic Semiparametric Factors of Volatility Strings," SFB 649 Discussion Papers SFB649DP2006-011, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  10. Han Shang, 2014. "A survey of functional principal component analysis," AStA Advances in Statistical Analysis, Springer, vol. 98(2), pages 121-142, April.
  11. T. F. Coleman & Y. Kim & Y. Li & M. Patron, 2007. "Robustly Hedging Variable Annuities With Guarantees Under Jump and Volatility Risks," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(2), pages 347-376.
  12. Francesco Audrino & Dominik Colangelo, 2009. "Option trading strategies based on semi-parametric implied volatility surface prediction," University of St. Gallen Department of Economics working paper series 2009 2009-24, Department of Economics, University of St. Gallen.
  13. Carol Alexander & Leonardo M. Nogueira, 2004. "Hedging with Stochastic and Local Volatility," ICMA Centre Discussion Papers in Finance icma-dp2004-10, Henley Business School, Reading University, revised Dec 2004.
  14. Laurini, Márcio P., 2007. "Imposing No-Arbitrage Conditions In Implied Volatility Surfaces Using Constrained Smoothing Splines," Insper Working Papers wpe_89, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.
  15. 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.
  16. Matthias Fengler & Wolfgang Härdle & Enno Mammen, 2005. "A Dynamic Semiparametric Factor Model for Implied Volatility String Dynamics," SFB 649 Discussion Papers SFB649DP2005-020, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  17. Szymon Borak & Matthias Fengler & Wolfgang Härdle, 2005. "DSFM fitting of Implied Volatility Surfaces," SFB 649 Discussion Papers SFB649DP2005-022, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  18. Michal Benko & Wolfgang Härdle & Alois Kneip, 2006. "Common Functional Principal Components," SFB 649 Discussion Papers SFB649DP2006-010, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  19. Mónica Fuentes & Sergio Godoy, 2005. "Sovereign Spread in Emerging Markets: A Principal Component Analysis," Working Papers Central Bank of Chile 333, Central Bank of Chile.
  20. George Skiadopoulos & Dimitris Psychoyios, 2006. "Implied Volatility Process: Evidence from the Volatility Derivatives Markets," Working Papers wpn06-17, Warwick Business School, Finance Group.

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