Calibration of self-decomposable Lévy models

Mathias Trabs

No 2011-073, SFB 649 Discussion Papers from Humboldt University Berlin, Collaborative Research Center 649: Economic Risk

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.

Keywords: adaptation; European option; infinite activity jump process; minimax rates; non linear inverse problem; self-decomposability. (search for similar items in EconPapers)
JEL-codes: C14 G13 (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (1)

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