Common Functional Principal Components
Functional principal component analysis (FPCA) based on the Karhunen-Lo`eve decomposition has been successfully applied in many applications, mainly for one sample problems. In this paper we consider common functional principal components for two sample problems. Our research is motivated not only by the theoretical challenge of this data situation but also by the actual question of dynamics of implied volatility (IV) functions. For different maturities the logreturns of IVs are samples of (smooth) random functions and the methods proposed here study the similarities of their stochastic behavior. Firstly we present a new method for estimation of functional principal components from discrete noisy data. Next we present the two sample inference for FPCA and develop two sample theory. We propose bootstrap tests for testing the equality of eigenvalues, eigenfunctions, and mean functions of two functional samples, illustrate the test-properties by simulation study and apply the method to the IV analysis.
|Date of creation:||Jan 2006|
|Contact details of provider:|| Postal: Spandauer Str. 1,10178 Berlin|
Web page: http://sfb649.wiwi.hu-berlin.de
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- Matthias Fengler & Wolfgang Härdle & Christophe Villa, 2003.
"The Dynamics of Implied Volatilities: A Common Principal Components Approach,"
Review of Derivatives Research,
Springer, vol. 6(3), pages 179-202, October.
- Christophe Villa & M.R. Fengler & W.K. Hardle, 2003. "The dynamics of implied volatilities : a common principal components approach," Post-Print halshs-00069509, HAL.
- Fengler, Matthias R. & Härdle, Wolfgang K. & Villa, Christophe, 2001. "The dynamics of implied volatilities: A common principal components approach," SFB 373 Discussion Papers 2001,38, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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- Matthias R. Fengler, 2005.
"Arbitrage-Free Smoothing of the Implied Volatility Surface,"
SFB 649 Discussion Papers
SFB649DP2005-019, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Matthias Fengler, 2009. "Arbitrage-free smoothing of the implied volatility surface," Quantitative Finance, Taylor & Francis Journals, vol. 9(4), pages 417-428.
- Dauxois, J. & Pousse, A. & Romain, Y., 1982. "Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 136-154, March.
- Matthias Fengler & Wolfgang Härdle & Enno Mammen, 2005. "A Dynamic Semiparametric Factor Model for Implied Volatility String Dynamics," SFB 649 Discussion Papers SFB649DP2005-020, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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