Multivariate Marked Poisson Processes and Market Related Multidimensional Information Flows

21 Pages Posted: 28 Dec 2016 Last revised: 18 Feb 2017

See all articles by Petar Jevtic

Petar Jevtic

McMaster University - Department of Mathematics and Statistics

Marina Marena

University of Eastern Piedmont

Patrizia Semeraro

Politecnico of Turin

Date Written: January 12, 2017

Abstract

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.

Keywords: marked Poisson processes, subordinated Lévy processes, multivariate Poisson random measure, multivariate subordinators, multivariate asset modelling, multivariate variance gamma process

JEL Classification: G12, G13

Suggested Citation

Jevtic, Petar and Marena, Marina and Semeraro, Patrizia, Multivariate Marked Poisson Processes and Market Related Multidimensional Information Flows (January 12, 2017). Available at SSRN: https://ssrn.com/abstract=2890521 or http://dx.doi.org/10.2139/ssrn.2890521

Petar Jevtic (Contact Author)

McMaster University - Department of Mathematics and Statistics ( email )

1280 Main Street West
Hamilton, Ontario L8S 4M4
Canada

Marina Marena

University of Eastern Piedmont ( email )

Corso Borsalino 50
Department of Economics and Quantitative Methods
15100 Alessandria
Italy
+39 011 6706275 (Phone)

Patrizia Semeraro

Politecnico of Turin ( email )

Torino, Turin - Piedmont 10100
Italy

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