Principal Components Analysis in implied volatility modeling (Analiza skladowych glownych w modelowaniu implikowanej zmiennosci)

Rafał Weron and Slawomir Wojcik

No HSC/04/03, HSC Research Reports from Hugo Steinhaus Center, Wroclaw University of Science and Technology

Abstract: We analyze the implied volatility surface structure of ODAX options as traded on DTB (currently Eurex). We apply PCA to cross sections of the implied volatility surface taken along the same moneyness (m) or the same time to maturity (T). For data from the period October 3rd 1997 – November 30th 1998 a substantial reduction of the dimensionality of the problem was achieved. It turned out that (i) for the m-sections the first two principal components contained 99.997% of information, and (ii) for the T-sections the first three principal components contained 99.892% of information. Moreover, the obtained principal components were very similar for different m's or T's allowing us to assume that that the space spanned by the eigenvectors is identical across several groups (of m's or T's), i.e. leading us to the so called Common PCA.

Keywords: Volatility surface; ODAX option; Principal Component Analysis; Common PCA (search for similar items in EconPapers)
JEL-codes: C38 G13 (search for similar items in EconPapers)
Pages: 11 pages
Date: 2004
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Published in Prace Naukowe Akademii Ekonomicznej we Wroc³awiu 1037 (2004) 315-324, in Polish.

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