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The dynamics of implied volatilities: A common principle components approach

Matthias Fengler, Wolfgang K. Härdle & Christophe Villa

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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.
   
type journal paper
   
keywords common principal component Analysis, principal component Analysis, factor model, implied volatility surface, smile
   
language English
kind of paper journal article
date of appearance 1-1-2003
journal Review of Derivatives Research
publisher Springer
ISSN 1380-6645
DOI 10.1023/B:REDR.0000004823.77464.2d
volume of journal 6
number of issue 3
page(s) 179-202
review double-blind review
   
citation Fengler, M., Härdle, W. K., & Villa, C. (2003). The dynamics of implied volatilities: A common principle components approach. Review of Derivatives Research, 6(3), 179-202, DOI:10.1023/B:REDR.0000004823.77464.2d.