Estimation of multivariate Lévy models via linear transformation by GMM

After a detailed introduction about the definition and the properties of Levy processes, the most important multivariate Lévy models available in the literature used for financial modelling are listed: in particular, the multivariate Lévy process via linear transformation introduced by Ballotta and Bonfiglioli (2014) in its Variance Gamma and Normal Inverse Gaussian specifications. The model is then calibrated to a dataset of ten MSCI stock indices from January 2009 to May 2013. The model is calibrated used the estimation technique called Generalized Method of Moments and the Spectral Generalized Method of Moments, widely described in the thesis. The simulation of the path of the process is also proposed. Finally, two tests are described, used to evaluate the marginal behavior of the calibration of the moments of one asset and the joint behavior of the calibration of the moments of the two assets.