The Dynamics of Implied Volatilities: A Common Principal Components Approach

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 anal...

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Bibliographic Details
Published in:Review of derivatives research 2003, Vol.6 (3), p.179-202
Main Authors: Fengler, Matthias R., Härdle, Wolfgang K., Villa, Christophe
Format: Article
Language:English
Subjects:
Business administration
Derivatives
Humanities and Social Sciences
Interest rates
Principal components analysis
Securities analysis
Securities prices
Studies
Time series
Volatility
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Summary: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. [PUBLICATION ABSTRACT]
ISSN:1380-6645
1573-7144
DOI:10.1023/B:REDR.0000004823.77464.2d