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Potential PCA interpretation problems for volatility smile dynamics

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  • Reiswich, Dimitri
  • Tompkins, Robert
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    Abstract

    Principal Component Analysis (PCA) is a common procedure for the analysis of financial market data, such as implied volatility smiles or interest rate curves. Recently, Pelsser and Lord [11] raised the question whether PCA results may not be 'facts but artefacts'. We extend this line of research by considering an alternative matrix structure which is consistent with foreign exchange option markets. For this matrix structure, PCA effects which are interpreted as shift, skew and curvature can be generated from unstructured random processes. Furthermore, we find that even if a structured system exists, PCA may not be able to distinguish between these three effects. The contribution of the factors explaining the variance in the original system are incorrect. Finally, for a special case, we provide an analytic correction that recovers correct factor variances from those incorrectly estimated by PCA. --

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    Bibliographic Info

    Paper provided by Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF) in its series CPQF Working Paper Series with number 19.

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    Date of creation: 2009
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    Handle: RePEc:zbw:cpqfwp:19

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    Keywords: Principal Component Analysis; PCA; Level; Slope; Curvature; Twist; Bisymmetric Matrices; Centro-symmetric Matrices;

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    1. Ansgar Belke & Thorsten Polleit, 2007. "How the ECB and the US Fed set interest rates," Applied Economics, Taylor & Francis Journals, vol. 39(17), pages 2197-2209.
    2. Hirsch, Christian & Bannier, Christina E., 2007. "The economics of rating watchlists: evidence from rating changes," Frankfurt School - Working Paper Series 88, Frankfurt School of Finance and Management.
    3. Christina Bannier, 2007. "Heterogeneous multiple bank financing: does it reduce inefficient credit-renegotiation incidences?," Financial Markets and Portfolio Management, Springer, vol. 21(4), pages 445-470, December.
    4. Bannier, Christina E., 2009. "Is there a hold-up benefit in heterogeneous multiple bank financing?," Frankfurt School - Working Paper Series 117, Frankfurt School of Finance and Management.
    5. Roßbach, Peter & Gießamer, Dirk, 2009. "Ein eLearning-System zur Unterstützung der Wissensvermittlung von Web-Entwicklern in Sicherheitsthemen," Frankfurt School - Working Paper Series 116, Frankfurt School of Finance and Management.
    6. Schanz, Kay-Michael & Schalast, Christoph, 2006. "Wertpapierprospekte: Markteinführungspublizität nach EU-Prospektverordnung und Wertpapierprospektgesetz 2005," Frankfurt School - Working Paper Series 74, Frankfurt School of Finance and Management.
    7. Bannier, Christina E. & Hänsel, Dennis N., 2007. "Determinants of banks' engagement in loan securitization," Frankfurt School - Working Paper Series 85, Frankfurt School of Finance and Management.
    8. Roßbach, Peter, 2009. "Die Rolle des Internets als Informationsbeschaffungsmedium in Banken," Frankfurt School - Working Paper Series 120, Frankfurt School of Finance and Management.
    9. Wollersheim, Jutta & Barthel, Erich, 2008. "Kulturunterschiede bei Mergers & Acquisitions: Entwicklung eines Konzeptes zur Durchführung einer Cultural Due Diligence," Frankfurt School - Working Paper Series 94, Frankfurt School of Finance and Management.
    10. Ansgar Belke & Thorsten Polleit, 2005. "(How) Do Stock Market Returns React to Monetary Policy? - An ARDL Cointegration Analysis for Germany," Diskussionspapiere aus dem Institut für Volkswirtschaftslehre der Universität Hohenheim 253/2005, Department of Economics, University of Hohenheim, Germany.
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