IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2005.06390.html
   My bibliography  Save this paper

Multivariate non-Gaussian models for financial applications

Author

Listed:
  • Michele Leonardo Bianchi
  • Asmerilda Hitaj
  • Gian Luca Tassinari

Abstract

In this paper we consider several continuous-time multivariate non-Gaussian models applied to finance and proposed in the literature in the last years. We study the models focusing on the parsimony of the number of parameters, the properties of the dependence structure, and the computational tractability. For each model we analyze the main features, we provide the characteristic function, the marginal moments up to order four, the covariances and the correlations. Thus, we describe how to calibrate them on the time-series of log-returns with a view toward practical applications and possible numerical issues. To empirically compare these models, we conduct an analysis on a five-dimensional series of stock index log-returns.

Suggested Citation

  • Michele Leonardo Bianchi & Asmerilda Hitaj & Gian Luca Tassinari, 2020. "Multivariate non-Gaussian models for financial applications," Papers 2005.06390, arXiv.org.
  • Handle: RePEc:arx:papers:2005.06390
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2005.06390
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Bianchi, Michele Leonardo & Rachev, Svetlozar T. & Kim, Young Shin & Fabozzi, Frank J., 2011. "Tempered infinitely divisible distributions and processes," Working Paper Series in Economics 26, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    3. Dilip B. Madan, 2018. "Instantaneous portfolio theory," Quantitative Finance, Taylor & Francis Journals, vol. 18(8), pages 1345-1364, August.
    4. Rathgeber, A.W. & Stadler, J. & Stöckl, S., 2019. "Financial modelling applying multivariate Lévy processes: New insights into estimation and simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 532(C).
    5. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    6. Lo, Andrew W & Wang, Jiang, 2000. "Trading Volume: Definitions, Data Analysis, and Implications of Portfolio Theory," The Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 257-300.
    7. Michele Leonardo Bianchi & Gian Luca Tassinari, 2020. "Forward-looking portfolio selection with multivariate non-Gaussian models," Quantitative Finance, Taylor & Francis Journals, vol. 20(10), pages 1645-1661, October.
    8. Marco Corazza & Florence Legros & Cira Perna & Marilena Sibillo, 2017. "Mathematical and Statistical Methods for Actuarial Sciences and Finance," Post-Print hal-01776135, HAL.
    9. Harris, Lawrence, 1986. "Cross-Security Tests of the Mixture of Distributions Hypothesis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(1), pages 39-46, March.
    10. Yves Dominicy & Hiroaki Ogata & David Veredas, 2013. "Inference for vast dimensional elliptical distributions," Computational Statistics, Springer, vol. 28(4), pages 1853-1880, August.
    11. Andreas Rathgeber & Johannes Stadler & Stefan Stöckl, 2019. "Financial modelling applying multivariate Levy processes: new insights into the estimation and simulation," Post-Print hal-01512848, HAL.
    12. Asmerilda Hitaj & Friedrich Hubalek & Lorenzo Mercuri & Edit Rroji, 2016. "Multivariate Mixed Tempered Stable Distribution," Papers 1609.00926, arXiv.org, revised Oct 2016.
    13. 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.
    14. Elisa Luciano & Wim Schoutens, 2006. "A multivariate jump-driven financial asset model," Quantitative Finance, Taylor & Francis Journals, vol. 6(5), pages 385-402.
    15. Hitaj, Asmerilda & Mercuri, Lorenzo & Rroji, Edit, 2015. "Portfolio selection with independent component analysis," Finance Research Letters, Elsevier, vol. 15(C), pages 146-159.
    16. Asmerilda Hitaj & Lorenzo Mercuri, 2013. "Portfolio allocation using multivariate variance gamma models," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 27(1), pages 65-99, March.
    17. Christian Genest & Michel Gendron & Michaël Bourdeau-Brien, 2009. "The Advent of Copulas in Finance," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 609-618.
    18. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    19. 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.
    20. Michele Leonardo Bianchi & Stoyan V Stoyanov & Gian Luca Tassinari & Frank J Fabozzi & Sergio M Focardi, 2019. "Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 11118.
    21. Chaussé, Pierre, 2010. "Computing Generalized Method of Moments and Generalized Empirical Likelihood with R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 34(i11).
    22. Elisa Luciano & Patrizia Semeraro, 2010. "A Generalized Normal Mean-Variance Mixture For Return Processes In Finance," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 415-440.
    23. Reiichiro Kawai, 2009. "A multivariate Levy process model with linear correlation," Quantitative Finance, Taylor & Francis Journals, vol. 9(5), pages 597-606.
    24. Michele Leonardo Bianchi & Giovanni De Luca & Giorgia Rivieccio, 2020. "CoVaR with volatility clustering, heavy tails and non-linear dependence," Papers 2009.10764, arXiv.org.
    25. Loregian, Angela & Mercuri, Lorenzo & Rroji, Edit, 2012. "Approximation of the variance gamma model with a finite mixture of normals," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 217-224.
    26. Elisa Luciano & Marina Marena & Patrizia Semeraro, 2016. "Dependence calibration and portfolio fit with factor-based subordinators," Quantitative Finance, Taylor & Francis Journals, vol. 16(7), pages 1037-1052, July.
    27. Bedendo, Mascia & Campolongo, Francesca & Joossens, Elisabeth & Saita, Francesco, 2010. "Pricing multiasset equity options: How relevant is the dependence function?," Journal of Banking & Finance, Elsevier, vol. 34(4), pages 788-801, April.
    28. Markus Michaelsen & Alexander Szimayer, 2018. "Marginal consistent dependence modelling using weak subordination for Brownian motions," Quantitative Finance, Taylor & Francis Journals, vol. 18(11), pages 1909-1925, November.
    29. Laura Ballotta & Efrem Bonfiglioli, 2016. "Multivariate asset models using Lévy processes and applications," The European Journal of Finance, Taylor & Francis Journals, vol. 22(13), pages 1320-1350, October.
    30. Ballotta, Laura & Fusai, Gianluca & Loregian, Angela & Perez, M. Fabricio, 2019. "Estimation of Multivariate Asset Models with Jumps," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 54(5), pages 2053-2083, October.
    31. Lorenzo Mercuri & Edit Rroji, 2018. "Risk parity for Mixed Tempered Stable distributed sources of risk," Annals of Operations Research, Springer, vol. 260(1), pages 375-393, January.
    32. Boris Buchmann & Kevin W. Lu & Dilip B. Madan, 2019. "Calibration for Weak Variance-Alpha-Gamma Processes," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1151-1164, December.
    33. Gian Luca Tassinari & Corrado Corradi, 2013. "Pricing equity and debt tranches of collateralized funds of hedge fund obligations: An approach based on stochastic time change and Esscher-transformed martingale measure," Quantitative Finance, Taylor & Francis Journals, vol. 13(12), pages 1991-2010, December.
    34. Rosinski, Jan, 2007. "Tempering stable processes," Stochastic Processes and their Applications, Elsevier, vol. 117(6), pages 677-707, June.
    35. Patrizia Semeraro, 2008. "A Multivariate Variance Gamma Model For Financial Applications," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 1-18.
    36. 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.
    37. 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.
    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. Michele Leonardo Bianchi & Giovanni De Luca & Giorgia Rivieccio, 2020. "CoVaR with volatility clustering, heavy tails and non-linear dependence," Papers 2009.10764, arXiv.org.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Elisa Luciano & Marina Marena & Patrizia Semeraro, 2013. "Dependence Calibration and Portfolio Fit with FactorBased Time Changes," Carlo Alberto Notebooks 307, Collegio Carlo Alberto, revised 2015.
    6. Boris Buchmann & Kevin W. Lu & Dilip B. Madan, 2019. "Calibration for Weak Variance-Alpha-Gamma Processes," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1151-1164, December.
    7. 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.
    8. Boris Buchmann & Benjamin Kaehler & Ross Maller & Alexander Szimayer, 2015. "Multivariate Subordination using Generalised Gamma Convolutions with Applications to V.G. Processes and Option Pricing," Papers 1502.03901, arXiv.org, revised Oct 2016.
    9. 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.
    10. Lynn Boen & Florence Guillaume, 2020. "Towards a $$\Delta $$Δ-Gamma Sato multivariate model," Review of Derivatives Research, Springer, vol. 23(1), pages 1-39, April.
    11. 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.
    12. M. Gardini & P. Sabino & E. Sasso, 2021. "The Variance Gamma++ Process and Applications to Energy Markets," Papers 2106.15452, arXiv.org.
    13. Asmerilda Hitaj & Friedrich Hubalek & Lorenzo Mercuri & Edit Rroji, 2016. "Multivariate Mixed Tempered Stable Distribution," Papers 1609.00926, arXiv.org, revised Oct 2016.
    14. Lorenzo Mercuri & Edit Rroji, 2018. "Risk parity for Mixed Tempered Stable distributed sources of risk," Annals of Operations Research, Springer, vol. 260(1), pages 375-393, January.
    15. Petar Jevtić & Marina Marena & Patrizia Semeraro, 2019. "Multivariate Marked Poisson Processes And Market Related Multidimensional Information Flows," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 1-26, March.
    16. Florence Guillaume, 2018. "Multivariate Option Pricing Models With Lévy And Sato Vg Marginal Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-26, March.
    17. Petar Jevtic & Patrizia Semeraro, 2014. "A class of multivariate marked Poisson processes to model asset returns," Carlo Alberto Notebooks 351, Collegio Carlo Alberto.
    18. Jie Chen & Liaoyuan Fan & Lingfei Li & Gongqiu Zhang, 2022. "A multidimensional Hilbert transform approach for barrier option pricing and survival probability calculation," Review of Derivatives Research, Springer, vol. 25(2), pages 189-232, July.
    19. Boris Buchmann & Kevin W. Lu & Dilip B. Madan, 2018. "Calibration for Weak Variance-Alpha-Gamma Processes," Papers 1801.08852, arXiv.org, revised Jul 2018.
    20. Patrizia Semeraro, 2022. "Multivariate tempered stable additive subordination for financial models," Mathematics and Financial Economics, Springer, volume 16, number 3, June.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:arx:papers:2005.06390. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.