The dynamics of implied volatilities: A common principal components approach
AbstractIt is common practice to identify the number and sources of shocks that move implied volatilities across space and time by applying Principal Components Analysis (PCA) to pooled covariance matrices of changes in implied volatilities. This approach, however, is likely to result in a loss of information, since the surface structure of implied volatilities in the maturities and moneyness dimension is neglected. In this paper we propose to estimate the implied volatility surface at each point in time nonparametrically and to analyze the implied volatility surface slice by slice with a common principal components analysis (CPCA). As opposed to traditional PCA, the basic assumption of CPCA is that the space spanned by the eigenvectors is identical across groups, whereas variances associated with the components are allowed to vary. This allows us to study a p variate random vector of k groups, say the volatility smile at p different grid points of moneyness for k maturities, simultaneously. Our evidence suggests that surface dynamics can indeed be traced back to a common eigenstructure between covariance matrices of the surface slices, which allow for the usual shift, slope, and twist interpretation of shocks to implied volatilities. This insight is a suitable starting point for VaR Monte Carlo Simulations of delta-gamma neutral, vega sensitive option portfolios. --
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
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 2001,38.
Date of creation: 2001
Date of revision:
Common Principal Component Analysis; Implied Volatility Surface; Principal Component Analysis; Smile;
Other versions of this item:
- 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.
- 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
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- 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.
- 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.
- 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.
- Cizek, P. & Tamine, J. & Härdle, W.K., 2006. "Smoothed L-estimation of Regression Function," Discussion Paper 2006-20, Tilburg University, Center for Economic Research.
- Tamine, Julien & Čížek, Pavel & Härdle, Wolfgang, 2002. "Smoothed L-estimation of regression function," SFB 373 Discussion Papers 2002,88, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Michal Benko & Wolfgang Härdle & Alois Kneip, 2006. "Common Functional Principal Components," SFB 649 Discussion Papers SFB649DP2006-010, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Pavel Cizek & Karel Komorad, 2005. "Implied Trinomial Trees," SFB 649 Discussion Papers SFB649DP2005-007, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- George Skiadopoulos & Dimitris Psychoyios, 2006. "Implied Volatility Process: Evidence from the Volatility Derivatives Markets," Working Papers wpn06-17, Warwick Business School, Finance Group.
- Michal Benko & Alois Kneip, 2005. "Common functional component modelling," SFB 649 Discussion Papers SFB649DP2005-016, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- 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.
- 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.
- 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.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (ZBW - German National Library of Economics).
If references are entirely missing, you can add them using this form.