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Multi-tail generalized elliptical distributions for asset returns

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  • Sebastian Kring
  • Svetlozar T. Rachev
  • Markus Höchstötter
  • Frank J. Fabozzi
  • Michele Leonardo Bianchi

Abstract

In the study of asset returns, the preponderance of empirical evidence finds that return distributions are not normally distributed. Despite this evidence, non-normal multivariate modelling of asset returns does not appear to play an important role in asset management or risk management because of the complexity of estimating multivariate non-normal distributions from market return data. In this paper, we present a new subclass of generalized elliptical distributions for asset returns that is sufficiently user friendly, so that it can be utilized by asset managers and risk managers for modelling multivariate non-normal distributions of asset returns. For the distribution we present, which we call the multi-tail generalized elliptical distribution, we (1) derive the densities using results of the theory of generalized elliptical distributions and (2) introduce a function, which we label the tail function, to describe their tail behaviour. We test the model on German stock returns and find that (1) the multi-tail model introduced in the paper significantly outperforms the classical elliptical model and (2) the hypothesis of homogeneous tail behaviour can be rejected. Copyright © 2009 The Author(s). Journal compilation © Royal Economic Society 2009

Suggested Citation

  • Sebastian Kring & Svetlozar T. Rachev & Markus Höchstötter & Frank J. Fabozzi & Michele Leonardo Bianchi, 2009. "Multi-tail generalized elliptical distributions for asset returns," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 272-291, July.
    • Handle: RePEc:ect:emjrnl:v:12:y:2009:i:2:p:272-291
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    Citations

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    Cited by:

    1. Gian Luca Tassinari & Michele Leonardo Bianchi, 2014. "Calibrating The Smile With Multivariate Time-Changed Brownian Motion And The Esscher Transform," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1-34.
    2. Frahm, Gabriel & Jaekel, Uwe, 2010. "A generalization of Tyler's M-estimators to the case of incomplete data," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 374-393, February.
    3. Michele Leonardo Bianchi & Gian Luca Tassinari, 2018. "Forward-looking portfolio selection with multivariate non-Gaussian models and the Esscher transform," Papers 1805.05584, arXiv.org, revised May 2018.
    4. Simon Hediger & Jeffrey Näf & Marc S. Paolella & Paweł Polak, 2023. "Heterogeneous tail generalized common factor modeling," Digital Finance, Springer, vol. 5(2), pages 389-420, June.
    5. Michele Leonardo Bianchi & Gian Luca Tassinari & Frank J. Fabozzi, 2016. "Riding With The Four Horsemen And The Multivariate Normal Tempered Stable Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-28, June.
    6. Michele Leonardo Bianchi & Asmerilda Hitaj & Gian Luca Tassinari, 2020. "Multivariate non-Gaussian models for financial applications," Papers 2005.06390, arXiv.org.

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