In this paper we propose a multivariate asset model based on L´evy processes for pricing of products written on more than one underlying asset. Our construction is based on a two factor representation of the dynamics of the asset log-returns. We investigate the properties of the model and introduce a multivariate generalization of some processes which are quite common in financial applications, such as subordinated Brownian motions, jump diffusion processes and time changed L´evy processes. Finally, we explore the issue of model calibration for the proposed setting and illustrate its robustness on a number of numerical examples
