A class of multivariate marked Poisson processes to model asset returns

This paper constructs a class of multivariate Gaussian marked Poisson processes to model asset returns. The model proposed accommodates the cross section properties of trades, allows for returns to be correlated conditional on trading activity, and preserves the economic intuition of normality of returns conditional on trading activity. We prove that the new class of processes are in law subordinated Brownian motions and we provide their characteristic function and correlation matrix in closed form. As a first application we specify a process of variance gamma type and show that, under suitable conditions, we find as subcases some of the well known multivariate variance gamma processes recently introduced in the financial literature.