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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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    Citations

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    Cited by:

    1. Cheng Peng & Young Shin Kim & Stefan Mittnik, 2022. "Portfolio Optimization on Multivariate Regime-Switching GARCH Model with Normal Tempered Stable Innovation," JRFM, MDPI, vol. 15(5), pages 1-23, May.
    2. Michele Leonardo Bianchi & Giovanni De Luca & Giorgia Rivieccio, 2020. "CoVaR with volatility clustering, heavy tails and non-linear dependence," Papers 2009.10764, arXiv.org.
    3. Asmerilda Hitaj & Lorenzo Mercuri & Edit Rroji, 2019. "Sensitivity analysis of Mixed Tempered Stable parameters with implications in portfolio optimization," Computational Management Science, Springer, vol. 16(1), pages 71-95, February.
    4. Young Shin Kim, 2022. "Portfolio optimization and marginal contribution to risk on multivariate normal tempered stable model," Annals of Operations Research, Springer, vol. 312(2), pages 853-881, May.
    5. 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.
    6. Michele Leonardo Bianchi & Alberto Maria Sorrentino, 2020. "Measuring CoVaR: An Empirical Comparison," Computational Economics, Springer;Society for Computational Economics, vol. 55(2), pages 511-528, February.
    7. Hasan Fallahgoul & Gregoire Loeper, 2021. "Modelling tail risk with tempered stable distributions: an overview," Annals of Operations Research, Springer, vol. 299(1), pages 1253-1280, April.
    8. Paolella, Marc S. & Polak, Paweł & Walker, Patrick S., 2019. "Regime switching dynamic correlations for asymmetric and fat-tailed conditional returns," Journal of Econometrics, Elsevier, vol. 213(2), pages 493-515.
    9. Michele Leonardo Bianchi & Asmerilda Hitaj & Gian Luca Tassinari, 2020. "Multivariate non-Gaussian models for financial applications," Papers 2005.06390, arXiv.org.
    10. Asmerilda Hitaj & Friedrich Hubalek & Lorenzo Mercuri & Edit Rroji, 2016. "Multivariate Mixed Tempered Stable Distribution," Papers 1609.00926, arXiv.org, revised Oct 2016.
    11. Hasan A. Fallahgoul & Young S. Kim & Frank J. Fabozzi & Jiho Park, 2019. "Quanto Option Pricing with Lévy Models," Computational Economics, Springer;Society for Computational Economics, vol. 53(3), pages 1279-1308, March.
    12. Bianchi, Michele Leonardo & De Luca, Giovanni & Rivieccio, Giorgia, 2023. "Non-Gaussian models for CoVaR estimation," International Journal of Forecasting, Elsevier, vol. 39(1), pages 391-404.

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