Implied volatility string dynamics
AbstractA 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 InfoPaper 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.
Date of creation: 2003
Date of revision:
Implied Volatility Surface; Smile; Generalized Additive Models; Backfitting; Functional Principal Component Analysis;
Find related papers by JEL classification:
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
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- 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.
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STICERD - Econometrics Paper Series
/2000/385, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
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- 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.
- 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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