Multivariate Asset Models Using Levy Processes and Applications

Abstract

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 Levy processes. Finally, we explore the issue of model calibration for the proposed setting and illustrate its robustness on a number of numerical examples.

Keywords: Jump Diffusion process, Levy processes, model calibration, multinames derivative contracts, subordinated Brownian motions, time changed Levy processes

JEL Classification: G13, G12, C63, D52