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Riding With The Four Horsemen And The Multivariate Normal Tempered Stable Model

Author

Listed:
  • MICHELE LEONARDO BIANCHI

    () (Regulation and Macroprudential Analysis Directorate, Bank of Italy, Via Milano 53, 00184 Rome, Italy)

  • GIAN LUCA TASSINARI

    () (School of Economics, Management and Statistics, Alma Mater Studiorum, University of Bologna, Piazza Scaravilli, 2, 40126 Bologna, Italy)

  • FRANK J. FABOZZI

    () (EDHEC Business School, 393, Promenade des Anglais, BP3116, 06202 Nice Cedex 3, France)

Abstract

In this paper, we study a model that captures four stylized facts about multivariate financial time series of equity returns: heavy tails, negative skew, asymmetric dependence, and volatility clustering (the four horsemen). The model is based on the multivariate normal tempered stable (MNTS) distribution, defined as the normal mean-variance mixture with a univariate tempered stable mixing distribution. To estimate the model, we propose a simple expectation–maximization maximum likelihood estimation procedure combined with the classical fast Fourier transform. The estimation algorithm is numerically reliable, and can be potentially used with a large number of assets. The method is applied to fit a five- and a 30-dimensional series of stock returns and to evaluate widely known portfolio risk measures. We analyzed the MNTS model with and without modeling the volatility clustering effect and compare the results with different models based on the multivariate normal and the multivariate generalized hyperbolic model.

Suggested Citation

  • 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.
  • Handle: RePEc:wsi:ijtafx:v:19:y:2016:i:04:n:s0219024916500278
    DOI: 10.1142/S0219024916500278
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    References listed on IDEAS

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    Cited by:

    1. repec:spr:comgts:v:16:y:2019:i:1:d:10.1007_s10287-018-0306-0 is not listed on IDEAS
    2. 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.
    3. repec:kap:compec:v:53:y:2019:i:3:d:10.1007_s10614-018-9807-8 is not listed on IDEAS

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