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A class of multivariate marked Poisson processes to model asset returns

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  • Petar Jevtic
  • Patrizia Semeraro

Abstract

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.

Suggested Citation

  • Petar Jevtic & Patrizia Semeraro, 2014. "A class of multivariate marked Poisson processes to model asset returns," Carlo Alberto Notebooks 351, Collegio Carlo Alberto.
    • Handle: RePEc:cca:wpaper:351
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    References listed on IDEAS

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    6. Patrizia Semeraro, 2006. "A Multivariate Time-Changed Lévy Model for Financial Applications," ICER Working Papers - Applied Mathematics Series 10-2006, ICER - International Centre for Economic Research.
    7. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    8. Thierry Ané & Hélyette Geman, 2000. "Order Flow, Transaction Clock, and Normality of Asset Returns," Journal of Finance, American Finance Association, vol. 55(5), pages 2259-2284, October.
    9. Patrizia Semeraro, 2008. "A Multivariate Variance Gamma Model For Financial Applications," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 1-18.
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    More about this item

    Keywords

    marked Poisson processes; subordinated Levy processes; multivariate Poisson ran- dom measure; multivariate subordinators; multivariate asset modelling; multivariate variance gamma process.;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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