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February 2014 Calibration of self-decomposable Lévy models
Mathias Trabs
Bernoulli 20(1): 109-140 (February 2014). DOI: 10.3150/12-BEJ478

Abstract

We study the nonparametric calibration of exponential Lévy models with infinite jump activity. In particular our analysis applies to self-decomposable processes 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, of the activity measure $\alpha:=k(0+)+k(0-)$ and of analogous parameters for the derivatives of the $k$-function are considered and on the other hand we estimate nonparametrically the $k$-function. Minimax convergence rates are derived. Since the rates depend on $\alpha$, we construct estimators adapting to this unknown parameter. Our estimation method is based on spectral representations of the observed option prices and on a regularization by cutting off high frequencies. Finally, the procedure is applied to simulations and real data.

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Mathias Trabs. "Calibration of self-decomposable Lévy models." Bernoulli 20 (1) 109 - 140, February 2014. https://doi.org/10.3150/12-BEJ478

Information

Published: February 2014
First available in Project Euclid: 22 January 2014

zbMATH: 1285.62101
MathSciNet: MR3160575
Digital Object Identifier: 10.3150/12-BEJ478

Keywords: Adaptation , European option , infinite activity jump process , Minimax rates , Nonlinear inverse problem , self-decomposability

Rights: Copyright © 2014 Bernoulli Society for Mathematical Statistics and Probability

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Vol.20 • No. 1 • February 2014
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