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Journal of Financial Econometrics Advance Access published online on March 12, 2007
Journal of Financial Econometrics, doi:10.1093/jjfinec/nbm005
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Copyright © The Author 2007. Published by Oxford University Press.

A semiparametric factor model for implied volatility surface dynamics

Matthias R. Fengler
     Sal. Oppenheim jr. & Cie.

Wolfgang K. Härdle
     Center for Applied Statistics and Economics

Enno Mammen
     University of Mannheim

Address correspondence to Matthias R. Fengler, Trading & Derivatives, Sal. Oppenheim jr. & Cie., Untermainanlage 1, 60329 Frankfurt am Main, Germany, or e-mail: matthias.fengler{at}oppenheim.de


  Abstract

We propose a semiparametric factor model, which approximates the implied volatility surface (IVS) in a finite dimensional function space. Unlike standard principal component approaches typically used to reduce complexity, our approach is tailored to the degenerated design of IVS data. In particular, we only fit in the local neighborhood of the design points by exploiting the expiry effect present in option data. Using DAX index option data, we estimate the nonparametric components and a low-dimensional time series of latent factors. The modeling approach is completed by studying vector autoregressive models fitted to the latent factors.

KEYWORDS: functional principal component analysis, implied volatility surface, semiparametric factor models

We gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft and the Sonderforschungsbereich 649 "Ökonomisches Risiko". We thank two anonymous referees, the editors, and Matthias Bode for their valuable comments and suggestions. The article represents the authors' personal opinion and does not reflect the views of Sal. Oppenheim.

Received February 28, 2006; revised September 21, 2006; accepted January 22, 2007


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