Spectral calibration of exponential Lévy models

@article{Belomestny2006SpectralCO,
  title={Spectral calibration of exponential L{\'e}vy models},
  author={Denis Belomestny and Markus Rei{\ss}},
  journal={Finance and Stochastics},
  year={2006},
  volume={10},
  pages={449-474}
}
We investigate the problem of calibrating an exponential Lévy model based on market prices of vanilla options. We show that this inverse problem is in general severely ill-posed and we derive exact minimax rates of convergence. The estimation procedure we propose is based on the explicit inversion of the option price formula in the spectral domain and a cut-off scheme for high frequencies as regularisation. 
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