Extending Time-Changed Lévy Asset Models Through Multivariate Subordinators

The traditional multivariate Lévy process constructed by subordinating a Brownian motion through a univariate subordinator presents a number of drawbacks, including the lack of independence and a limited range of dependence. In order to face these, we investigate multivariate subordination, with a common and an idiosyncratic component. We introduce generalizations of some well known univariate Lévy processes for financial applications: the multivariate compound Poisson, NIG, Variance Gamma and CGMY. In all these cases the extension is parsimonious, in that one additional parameter only is needed.First we characterize the subordinator, then the time changed processes via their Lévy measure and characteristic exponent. Finally we study the subordinator association, as well as the subordinated processes' linear and non linear dependence. We show that the processes generated with the proposed time change can include Independence and that they span the whole range of linear dependence. We provide some examples of simulated trajectories, scatter plots and both linear and non linear dependence measures. The input data for these simulations are calibrated values of major stock indices