Multivariate Marked Poisson Processes and Market Related Multidimensional Information Flows

We propose a new overarching interpretation of multidimensional information flows and their relation to market movements. The new conceptualization hinges on results of two distinct mathematical theories, Lévy processes and marked Poisson processes, bridged in Jevtić et al. (2016) and applied here in the context of finance, specifically in multivariate modelling of asset returns. Specifically, in this paper we construct 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 normality of returns conditional on trading activity. We specify a process of normal inverse Gaussian type and show that, under suitable conditions, we find as subcases some of the well known multivariate processes recently introduced in the financial literature. As a first application example we estimate a two dimensional price process on daily log-returns and perform a sensitivity analysis of the model parameters to show the model dependence structure flexibility.