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

Andreas Rathgeber, Johannes Stadler and Stefan Stöckl
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Andreas Rathgeber: UNIA - Universität Augsburg [Deutschland] = University of Augsburg [Germany] = Université d'Augsburg [Allemagne]
Johannes Stadler: UNIA - Universität Augsburg [Deutschland] = University of Augsburg [Germany] = Université d'Augsburg [Allemagne]
Stefan Stöckl: ICN Business School, CEREFIGE - Centre Européen de Recherche en Economie Financière et Gestion des Entreprises - UL - Université de Lorraine

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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.

Keywords: Levy processes; Financial Modelling (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

Published in Physica A: Statistical Mechanics and its Applications, 2019, 532, pp.121386. ⟨10.1016/j.physa.2019.121386⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01512848

DOI: 10.1016/j.physa.2019.121386

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