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Title:Calibration of self-decomposable Lévy models PDF Logo
Authors:Trabs, Mathias
Issue Date:2011
Series/Report no.:SFB 649 discussion paper 2011-073
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.
European option
infinite activity jump process
minimax rates
non linear inverse problem
Document Type:Working Paper
Appears in Collections:SFB 649 Discussion Papers, HU Berlin

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