Spectral calibration of exponential Lévy Models [1] - Denis Belomestny; Markus Reiß (Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk, 2006)
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.
Keywords: G13; C14; 330; European option; jump diffusion; minimax rates; severely ill-posed; nonlinear inverse problem; spectral cut-off