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Extending Time-Changed Lévy Asset Models Through Multivariate Subordinators

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  • Elisa Luciano
  • Patrizia Semeraro

Abstract

The traditional multivariate Lévy process constructed by subordinating a Brownian motion through a univariate subordinator presents a number of drawbacks, including the lack of independence and a limited range of dependence. In order to face these, we investigate multivariate subordination, with a common and an idiosyncratic component. We introduce generalizations of some well known univariate Lévy processes for financial applications: the multivariate compound Poisson, NIG, Variance Gamma and CGMY. In all these cases the extension is parsimonious, in that one additional parameter only is needed. We characterize first the subordinator, then the time changed processes via their Lévy measure and characteristic exponent. We further study the subordinator association, as well as the subordinated processes linear and non linear dependence. We show that the processes generated with the proposed time change can include independence and that they span the whole range of linear dependence. We provide some examples of simulated trajectories,scatter plots and both linear and non linear dependence measures. The input data for these simulations are calibrated values for major stock indices.

Suggested Citation

  • Elisa Luciano & Patrizia Semeraro, 2007. "Extending Time-Changed Lévy Asset Models Through Multivariate Subordinators," Carlo Alberto Notebooks 42, Collegio Carlo Alberto.
  • Handle: RePEc:cca:wpaper:42
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    File URL: http://www.carloalberto.org/assets/working-papers/no.42.pdf
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    References listed on IDEAS

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    1. Elisa Luciano & Wim Schoutens, 2006. "A multivariate jump-driven financial asset model," Quantitative Finance, Taylor & Francis Journals, vol. 6(5), pages 385-402.
    2. 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.
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    Cited by:

    1. Elisa Luciano & Patrizia Semeraro, 2007. "Generalized Normal Mean Variance Mixture and Subordinated Brownian Motion," ICER Working Papers - Applied Mathematics Series 42-2007, ICER - International Centre for Economic Research.
    2. Elisa Luciano & Patrizia Semeraro, 2010. "A Generalized Normal Mean-Variance Mixture For Return Processes In Finance," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 415-440.

    More about this item

    Keywords

    Lévy processes; multivariate subordinators; dependence (association; correlation); multivariate asset modelling;

    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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