Marina Marena

We introduce a class of multivariate factor-based processes with the dependence structure of Lévy ραρα-models and Sato marginal distributions. We focus on variance gamma and normal inverse Gaussian marginal specifications for their analytical tractability and fit properties. We explore if Sato models, whose margins incorporate more realistic moments term structures, preserve the correlation flexibility in fitting option data. Since ραρα-models incorporate nonlinear dependence, we also investigate the impact of Sato margins on nonlinear dependence and its evolution over time.

In this paper, we study factor-based subordinated Lévy processes in their variance gamma (VG) and normal inverse Gaussian (NIG) specifications, and focus on their ability to price multivariate exotic derivatives. Both model specifications, calibrated to a data set of multivariate barrier reverse convertibles listed at the Swiss market, demonstrate good ability in capturing smile patterns and recovering empirical correlations. We show how the range of correlations spanned by each model is linked to the process marginal distributions.

The class of marked Poisson processes and its connection with subordinated Lévy processes allow us to propose a new interpretation of multidimensional information flows and their relation to market movements. The new approach provides a unified framework for multivariate asset return models in a Lévy economy. In fact, we are able to recover several processes commonly used to model asset returns as subcases. We consider a first application example using the normal inverse Gaussian specification.