Implied volatility string dynamics
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.
|Date of creation:||2003|
|Date of revision:|
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- Christophe Villa & M.R. Fengler & W.K. Hardle, 2003.
"The dynamics of implied volatilities : a common principal components approach,"
- 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.
- Fengler, Matthias R. & Härdle, Wolfgang K. & Villa, Christophe, 2001. "The dynamics of implied volatilities: A common principal components approach," SFB 373 Discussion Papers 2001,38, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Oliver B. Linton & Enno Mammen & J. Nielsen & Carsten Tanggaard, 2000.
"Yield Curve Estimation by Kernel Smoothing Methods,"
Econometric Society World Congress 2000 Contributed Papers
0235, Econometric Society.
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- Oliver Linton & Enno Mammen & Jens Perch Nielsen & C Tanggaard, 2000. "Yield curve estimation by kernel smoothing methods," LSE Research Online Documents on Economics 2270, London School of Economics and Political Science, LSE Library.
- 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.
- Härdle, Wolfgang Karl & Blaskowitz, Oliver J. & Schmidt, Peter, 2004. "Skewness and Kurtosis Trades," Papers 2004,09, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE).
- Toby Daglish & John Hull & Wulin Suo, 2007. "Volatility surfaces: theory, rules of thumb, and empirical evidence," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 507-524.
- Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
- George Skiadopoulos & Stewart Hodges & Les Clewlow, 2000. "The Dynamics of the S&P 500 Implied Volatility Surface," Review of Derivatives Research, Springer, vol. 3(3), pages 263-282, October.
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