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Implied volatility string dynamics

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Author Info

  • Fengler, Matthias R.
  • Härdle, Wolfgang
  • Mammen, Enno

Abstract

A primary goal in modelling the dynamics of implied volatility surfaces (IVS) aims at reducing complexity. For this purpose one fits the IVS each day and applies a principal component analysis using a functional norm. This approach, however, neglects the degenerated string structure of the implied volatility data and may result in a severe modelling bias. We propose a dynamic semiparametric factor model, which approximates the IVS in a finite dimensional function space. The key feature is that we only fit in the local neighborhood of the design points. Our approach is a combination of methods from functional principal component analysis and backfitting techniques for additive models. The model is found to have an approximate 10% better performance than the typical näive trader models. The model can be a backbone in risk management serving for value at risk computations and scenario analysis. --

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Bibliographic Info

Paper provided by Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes in its series SFB 373 Discussion Papers with number 2003,54.

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Date of creation: 2003
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Handle: RePEc:zbw:sfb373:200354

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Related research

Keywords: Implied Volatility Surface; Smile; Generalized Additive Models; Backfitting; Functional Principal Component Analysis;

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References

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  1. 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.
  2. Oliver Linton & Enno Mammen & Jens Perch Nielsen & C Tanggaard, 2000. "Yield Curve Estimation by Kernel Smoothing Methods," STICERD - Econometrics Paper Series, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE /2000/385, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  3. George Skiadopoulos & Stewart Hodges & Les Clewlow, 2000. "The Dynamics of the S&P 500 Implied Volatility Surface," Review of Derivatives Research, Springer, Springer, vol. 3(3), pages 263-282, October.
  4. Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 2(1), pages 45-60.
  5. Toby Daglish & John Hull & Wulin Suo, 2007. "Volatility surfaces: theory, rules of thumb, and empirical evidence," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 7(5), pages 507-524.
  6. Härdle, Wolfgang Karl & Blaskowitz, Oliver J. & Schmidt, Peter, 2004. "Skewness and Kurtosis Trades," Papers, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE) 2004,09, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE).
  7. Matthias Fengler & Wolfgang Härdle & Christophe Villa, 2003. "The Dynamics of Implied Volatilities: A Common Principal Components Approach," Review of Derivatives Research, Springer, Springer, vol. 6(3), pages 179-202, October.
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