Spectral calibration of exponential Lévy ; 1

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 option price formula in the spectral domain and a cut-off scheme for high frequencies as regularisation. -- European option ; jump diffusion ; minimax rates ; severely ill-posed ; nonlinear inverse problem ; spectral cut-off