Multivariate time changes for Lévy asset models: Characterization and calibration

We build a theoretical framework for multivariate subordination of Brownian motions, with a common and an idiosyncratic component. This follows economic intuition and introduces generalizations of some well known multivariate Lévy processes for financial applications: the compound Poisson, NIG, Variance Gamma and CGMY. In most cases we obtain the characteristic function in closed form. The extension is first kept parsimonious, by adding one parameter only. The empirical fit of (linear) dependence is then increased, by allowing for dependent Brownian motions.