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Financial modelling applying multivariate Levy processes: new insights into the estimation and simulation

Author

Listed:
  • Andreas Rathgeber

    (UNIA - University of Augsburg)

  • Johannes Stadler

    (UNIA - University of Augsburg)

  • Stefan Stöckl

    (ICN Business School, CEREFIGE - Centre Européen de Recherche en Economie Financière et Gestion des Entreprises - UL - Université de Lorraine)

Abstract

In general, daily or intra-day stock returns are fat-tailed and heavily skewed. Lévy processes fulfil these modelling requirements and produce marginal distributions with finite variances. An extensive body of literature looks into the fittings and applications of single processes. In contrast, our analysis of multivariate Lévy models finds applications in pricing multivariate options or in portfolio and risk management. We use the technique of multivariate subordination and conduct a large simulation study on the fitting of the GH, NIG, and VG models in order to identify the best fitting method for multivariate Lévy processes, as well as the best multivariate model overall. Our findings confirm previous results in the literature, namely that the MLE is the best estimation approach in a two-step fitting procedure and the GH model is the best multivariate model. It reveals that also the method is appropriate.

Suggested Citation

  • Andreas Rathgeber & Johannes Stadler & Stefan Stöckl, 2019. "Financial modelling applying multivariate Levy processes: new insights into the estimation and simulation," Post-Print hal-01512848, HAL.
    • Handle: RePEc:hal:journl:hal-01512848
    DOI: 10.1016/j.physa.2019.121386
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    Cited by:

    1. Michele Leonardo Bianchi & Asmerilda Hitaj & Gian Luca Tassinari, 2020. "Multivariate non-Gaussian models for financial applications," Papers 2005.06390, arXiv.org.
    2. Ulze, Markus & Stadler, Johannes & Rathgeber, Andreas W., 2021. "No country for old distributions? On the comparison of implied option parameters between the Brownian motion and variance gamma process," The Quarterly Review of Economics and Finance, Elsevier, vol. 82(C), pages 163-184.

    More about this item

    Keywords

    Levy processes; Financial Modelling;

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