Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/148869
Authors: 
Grith, Maria
Härdle, Wolfgang
Kneip, Alois
Wagner, Heiko
Year of Publication: 
2016
Series/Report no.: 
SFB 649 Discussion Paper 2016-033
Abstract: 
We present two methods based on functional principal component analysis (FPCA) for the estimation of smooth derivatives of a sample of random functions, which are observed in a more than one-dimensional domain.We apply eigenvalue decomposition to a) the dual covariance matrix of the derivatives, and b) the dual covariance matrix of the observed curves. To handle noisy data from discrete observations, we rely on local polynomial regressions. If curves are contained in a finite-dimensional function space, the secondmethod performs better asymptotically. We apply our methodology in a simulation and empirical study, inwhichwe estimate state price density (SPD) surfaces from call option prices.We identify three main components, which can be interpreted as volatility, skewness and tail factors.We also find evidence for term structure variation.
Subjects: 
functional principal component
dual method
derivatives
multivariate functions
state price densities
JEL: 
C13
C14
G13
Document Type: 
Working Paper

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