Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/56680 
Authors: 
Year of Publication: 
2011
Series/Report no.: 
SFB 649 Discussion Paper No. 2011-073
Publisher: 
Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk, Berlin
Abstract: 
We study the nonparametric calibration of exponential, self-decomposable Lévy models whose jump density can be characterized by the k-function, which is typically nonsmooth at zero. On the one hand the estimation of the drift, the activity measure a := k(0+) + k(0-) and analog parameters for the derivatives are considered and on the other hand we estimate the k-function outside of a neighborhood of zero. Minimax convergence rates are derived, which depend on a. Therefore, we construct estimators adapting to this unknown parameter. Our estimation method is based on spectral representations of the observed option prices and on regularization by cutting off high frequencies. Finally, the procedure is applied to simulations and real data.
Subjects: 
adaptation
European option
infinite activity jump process
minimax rates
non linear inverse problem
self-decomposability.
JEL: 
C14
G13
Document Type: 
Working Paper

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