IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v19y2016i04ns0219024916500278.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024916500278
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024916500278?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Florence Guillaume, 2013. "The αVG model for multivariate asset pricing: calibration and extension," Review of Derivatives Research, Springer, vol. 16(1), pages 25-52, April.
    2. Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Science and Technology, number hsbook0501, December.
    3. Kim, Young Shin & Rachev, Svetlozar T. & Bianchi, Michele Leonardo & Mitov, Ivan & Fabozzi, Frank J., 2011. "Time series analysis for financial market meltdowns," Journal of Banking & Finance, Elsevier, vol. 35(8), pages 1879-1891, August.
    4. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    5. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    6. 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.
    7. Young Kim & Rosella Giacometti & Svetlozar Rachev & Frank Fabozzi & Domenico Mignacca, 2012. "Measuring financial risk and portfolio optimization with a non-Gaussian multivariate model," Annals of Operations Research, Springer, vol. 201(1), pages 325-343, December.
    8. Svetlana I. Boyarchenko & Sergei Z. Levendorskiǐ, 2000. "Option Pricing For Truncated Lévy Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 549-552.
    9. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    10. Paul Embrechts & Giovanni Puccetti & Ludger Rüschendorf & Ruodu Wang & Antonela Beleraj, 2014. "An Academic Response to Basel 3.5," Risks, MDPI, vol. 2(1), pages 1-24, February.
    11. Suzanne Emmer & Marie Kratz & Dirk Tasche, 2013. "What Is the Best Risk Measure in Practice? A Comparison of Standard Measures," Working Papers hal-00921283, HAL.
    12. Yves Dominicy & Hiroaki Ogata & David Veredas, 2013. "Inference for vast dimensional elliptical distributions," Computational Statistics, Springer, vol. 28(4), pages 1853-1880, August.
    13. Susanne Emmer & Marie Kratz & Dirk Tasche, 2013. "What is the best risk measure in practice? A comparison of standard measures," Papers 1312.1645, arXiv.org, revised Apr 2015.
    14. Rosinski, Jan, 2007. "Tempering stable processes," Stochastic Processes and their Applications, Elsevier, vol. 117(6), pages 677-707, June.
    15. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    16. Sergei Levendorskiĭ, 2012. "Efficient Pricing And Reliable Calibration In The Heston Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(07), pages 1-44.
    17. 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.
    18. Wenbo Hu & Alec Kercheval, 2010. "Portfolio optimization for student t and skewed t returns," Quantitative Finance, Taylor & Francis Journals, vol. 10(1), pages 91-105.
    19. Simon A. Broda & Marc S. Paolella, 2009. "CHICAGO: A Fast and Accurate Method for Portfolio Risk Calculation," Journal of Financial Econometrics, Oxford University Press, vol. 7(4), pages 412-436, Fall.
    20. repec:hal:journl:hal-00921283 is not listed on IDEAS
    21. Paolella, Marc S. & Polak, Paweł, 2015. "COMFORT: A common market factor non-Gaussian returns model," Journal of Econometrics, Elsevier, vol. 187(2), pages 593-605.
    22. Matthias Scherer & Svetlozar T. Rachev & Young Shin Kim & Frank J. Fabozzi, 2012. "Approximation of skewed and leptokurtic return distributions," Applied Financial Economics, Taylor & Francis Journals, vol. 22(16), pages 1305-1316, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Slim, Skander & Koubaa, Yosra & BenSaïda, Ahmed, 2017. "Value-at-Risk under Lévy GARCH models: Evidence from global stock markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 46(C), pages 30-53.
    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. 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.
    4. Sander Barendse & Erik Kole & Dick van Dijk, 2023. "Backtesting Value-at-Risk and Expected Shortfall in the Presence of Estimation Error," Journal of Financial Econometrics, Oxford University Press, vol. 21(2), pages 528-568.
    5. Enrique Molina‐Muñoz & Andrés Mora‐Valencia & Javier Perote, 2021. "Backtesting expected shortfall for world stock index ETFs with extreme value theory and Gram–Charlier mixtures," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(3), pages 4163-4189, July.
    6. Michele Leonardo Bianchi & Asmerilda Hitaj & Gian Luca Tassinari, 2020. "Multivariate non-Gaussian models for financial applications," Papers 2005.06390, arXiv.org.
    7. Anand, Abhinav & Li, Tiantian & Kurosaki, Tetsuo & Kim, Young Shin, 2016. "Foster–Hart optimal portfolios," Journal of Banking & Finance, Elsevier, vol. 68(C), pages 117-130.
    8. Fantazzini, Dean & Shangina, Tamara, 2019. "The importance of being informed: forecasting market risk measures for the Russian RTS index future using online data and implied volatility over two decades," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 55, pages 5-31.
    9. Kwangmin Jung & Donggyu Kim & Seunghyeon Yu, 2022. "Next generation models for portfolio risk management: An approach using financial big data," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(3), pages 765-787, September.
    10. Xu, Qifa & Chen, Lu & Jiang, Cuixia & Yu, Keming, 2020. "Mixed data sampling expectile regression with applications to measuring financial risk," Economic Modelling, Elsevier, vol. 91(C), pages 469-486.
    11. Hasan A. Fallahgoul & David Veredas & Frank J. Fabozzi, 2019. "Quantile-Based Inference for Tempered Stable Distributions," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 51-83, January.
    12. Argyropoulos, Christos & Panopoulou, Ekaterini, 2019. "Backtesting VaR and ES under the magnifying glass," International Review of Financial Analysis, Elsevier, vol. 64(C), pages 22-37.
    13. 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.
    14. Abhinav Anand & Tiantian Li & Tetsuo Kurosaki & Young Shin Kim, 2017. "The equity risk posed by the too-big-to-fail banks: a Foster–Hart estimation," Annals of Operations Research, Springer, vol. 253(1), pages 21-41, June.
    15. Michele Leonardo Bianchi & Giovanni De Luca & Giorgia Rivieccio, 2020. "CoVaR with volatility clustering, heavy tails and non-linear dependence," Papers 2009.10764, arXiv.org.
    16. Kratz, Marie & Lok, Yen H. & McNeil, Alexander J., 2018. "Multinomial VaR backtests: A simple implicit approach to backtesting expected shortfall," Journal of Banking & Finance, Elsevier, vol. 88(C), pages 393-407.
    17. Lazar, Emese & Zhang, Ning, 2019. "Model risk of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 105(C), pages 74-93.
    18. Peña, Juan Ignacio & Rodríguez, Rosa & Mayoral, Silvia, 2020. "Tail risk of electricity futures," Energy Economics, Elsevier, vol. 91(C).
    19. Timo Dimitriadis & Xiaochun Liu & Julie Schnaitmann, 2020. "Encompassing Tests for Value at Risk and Expected Shortfall Multi-Step Forecasts based on Inference on the Boundary," Papers 2009.07341, arXiv.org.
    20. Marie Kratz & Yen H Lok & Alexander J Mcneil, 2016. "Multinomial var backtests: A simple implicit approach to backtesting expected shortfall," Working Papers hal-01424279, HAL.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:ijtafx:v:19:y:2016:i:04:n:s0219024916500278. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.