IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v64y2024i1d10.1007_s10614-023-10457-5.html
   My bibliography  Save this article

A Review of Generalized Hyperbolic Distributions

Author

Listed:
  • Xiao Jiang

    (University of Manchester)

  • Saralees Nadarajah

    (University of Manchester)

  • Thomas Hitchen

    (University of Manchester)

Abstract

The generalized hyperbolic distributions are fast becoming the most popular models for financial returns. In recent years, many variants of generalized hyperbolic distributions have been proposed in the literature. This paper provides a review of generalized hyperbolic and related distributions, including software available for them. A simulation study and real data applications are presented to compare some of the reviewed distributions.

Suggested Citation

  • Xiao Jiang & Saralees Nadarajah & Thomas Hitchen, 2024. "A Review of Generalized Hyperbolic Distributions," Computational Economics, Springer;Society for Computational Economics, vol. 64(1), pages 595-624, July.
    • Handle: RePEc:kap:compec:v:64:y:2024:i:1:d:10.1007_s10614-023-10457-5
    DOI: 10.1007/s10614-023-10457-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10614-023-10457-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10614-023-10457-5?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. Ardia, David & Hoogerheide, Lennart F. & van Dijk, Herman K., 2009. "Adaptive Mixture of Student-t Distributions as a Flexible Candidate Distribution for Efficient Simulation: The R Package AdMit," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 29(i03).
    2. Xiangyu Han & Chuancun Yin, 2022. "Tail Conditional Moments for Location-Scale Mixture of Elliptical Distributions," Mathematics, MDPI, vol. 10(4), pages 1-21, February.
    3. Fred Espen Benth & Pål Nicolai Henriksen, 2011. "Pricing of basket options using univariate normal inverse gaussian approximations," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(3), pages 355-376, April.
    4. Chou-Wen Wang & Sharon S. Yang & Jr-Wei Huang, 2017. "Analytic option pricing and risk measures under a regime-switching generalized hyperbolic model with an application to equity-linked insurance," Quantitative Finance, Taylor & Francis Journals, vol. 17(10), pages 1567-1581, October.
    5. Josephine Dufitinema, 2021. "Stochastic volatility forecasting of the Finnish housing market," Applied Economics, Taylor & Francis Journals, vol. 53(1), pages 98-114, January.
    6. Leovardo Mata Mata & José Antonio Núñez Mora & Ramona Serrano Bautista, 2021. "Multivariate Distribution in the Stock Markets of Brazil, Russia, India, and China," SAGE Open, , vol. 11(2), pages 21582440211, April.
    7. Amiri , Hossein & Najafi Nejad , Mahmood & Mousavi , Seyede Mohadese, 2021. "Estimation of Value at Risk (VaR) Based On Lévy-GARCH Models: Evidence from Tehran Stock Exchange," Journal of Money and Economy, Monetary and Banking Research Institute, Central Bank of the Islamic Republic of Iran, vol. 16(2), pages 165-186, June.
    8. John R. Birge & L. Chavez-Bedoya, 2021. "Portfolio optimization under the generalized hyperbolic distribution: optimal allocation, performance and tail behavior," Quantitative Finance, Taylor & Francis Journals, vol. 21(2), pages 199-219, February.
    9. Nakajima, Jouchi & Omori, Yasuhiro, 2012. "Stochastic volatility model with leverage and asymmetrically heavy-tailed error using GH skew Student’s t-distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3690-3704.
    10. Rui Li & Saralees Nadarajah, 2020. "A review of Student’s t distribution and its generalizations," Empirical Economics, Springer, vol. 58(3), pages 1461-1490, March.
    11. André Lucas & Bernd Schwaab & Xin Zhang, 2014. "Conditional Euro Area Sovereign Default Risk," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(2), pages 271-284, April.
    12. Rowińska, Paulina A. & Veraart, Almut E.D. & Gruet, Pierre, 2021. "A multi-factor approach to modelling the impact of wind energy on electricity spot prices," Energy Economics, Elsevier, vol. 104(C).
    13. Fred Espen Benth & Jūratė Šaltytė-Benth, 2004. "The Normal Inverse Gaussian Distribution And Spot Price Modelling In Energy Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(02), pages 177-192.
    14. Callealta Barroso, Francisco Javier & García-Pérez, Carmelo & Prieto-Alaiz, Mercedes, 2020. "Modelling income distribution using the log Student’s t distribution: New evidence for European Union countries," Economic Modelling, Elsevier, vol. 89(C), pages 512-522.
    15. Oh Kang Kwon & Stephen Satchell, 2020. "The Distribution of Cross Sectional Momentum Returns When Underlying Asset Returns Are Student’s t Distributed," JRFM, MDPI, vol. 13(2), pages 1-19, February.
    16. Martin Burda & Matthew Harding & Jerry Hausman, 2015. "A Bayesian Semiparametric Competing Risk Model with Unobserved Heterogeneity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(3), pages 353-376, April.
    17. Makoto Nakakita & Teruo Nakatsuma, 2021. "Bayesian Analysis of Intraday Stochastic Volatility Models of High-Frequency Stock Returns with Skew Heavy-Tailed Errors," JRFM, MDPI, vol. 14(4), pages 1-29, March.
    18. Kuntadi, Cris, 2022. "Effective energy commodity risk management on Indonesia," Resources Policy, Elsevier, vol. 78(C).
    19. Abhinav Gupta & Karmeshu, 2015. "Study of compound generalized Nakagami–generalized inverse Gaussian distribution and related densities: application to ultrasound imaging," Computational Statistics, Springer, vol. 30(1), pages 81-96, March.
    20. José Antonio Núñez-Mora & Eduardo Sánchez-Ruenes, 2020. "Generalized Hyperbolic Distribution and Portfolio Efficiency in Energy and Stock Markets of BRIC Countries," IJFS, MDPI, vol. 8(4), pages 1-14, October.
    21. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    22. Lakshina, Valeriya, 2020. "Do portfolio investors need to consider the asymmetry of returns on the Russian stock market?," The Journal of Economic Asymmetries, Elsevier, vol. 21(C).
    23. Song, Shijia & Li, Handong, 2022. "Predicting VaR for China's stock market: A score-driven model based on normal inverse Gaussian distribution," International Review of Financial Analysis, Elsevier, vol. 82(C).
    24. Lemonte, Artur J. & Cordeiro, Gauss M., 2011. "The exponentiated generalized inverse Gaussian distribution," Statistics & Probability Letters, Elsevier, vol. 81(4), pages 506-517, April.
    25. Kjersti Aas & Ingrid Hobaek Haff, 2006. "The Generalized Hyperbolic Skew Student's t-Distribution," Journal of Financial Econometrics, Oxford University Press, vol. 4(2), pages 275-309.
    26. Lengua Lafosse, Patricia & Rodríguez, Gabriel, 2018. "An empirical application of a stochastic volatility model with GH skew Student's t-distribution to the volatility of Latin-American stock returns," The Quarterly Review of Economics and Finance, Elsevier, vol. 69(C), pages 155-173.
    27. Marcelo Ventura & Helton Saulo & Victor Leiva & Sandro Monsueto, 2019. "Log‐symmetric regression models: information criteria and application to movie business and industry data with economic implications," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 35(4), pages 963-977, July.
    28. Olivia Andreea Baciu, 2015. "Generalized Hyperbolic Distributions: Empirical Evidence on Bucharest Stock Exchange," The Review of Finance and Banking, Academia de Studii Economice din Bucuresti, Romania / Facultatea de Finante, Asigurari, Banci si Burse de Valori / Catedra de Finante, vol. 7(1), pages 007-018, June.
    29. David Scott & Diethelm Würtz & Christine Dong & Thanh Tran, 2011. "Moments of the generalized hyperbolic distribution," Computational Statistics, Springer, vol. 26(3), pages 459-476, September.
    30. Nitithumbundit, Thanakorn & Chan, Jennifer S.K., 2022. "Covid-19 impact on Cryptocurrencies market using Multivariate Time Series Models," The Quarterly Review of Economics and Finance, Elsevier, vol. 86(C), pages 365-375.
    31. Göncü, Ahmet & Yang, Hao, 2016. "Variance-Gamma and Normal-Inverse Gaussian models: Goodness-of-fit to Chinese high-frequency index returns," The North American Journal of Economics and Finance, Elsevier, vol. 36(C), pages 279-292.
    32. Flora, Maria & Vargiolu, Tiziano, 2020. "Price dynamics in the European Union Emissions Trading System and evaluation of its ability to boost emission-related investment decisions," European Journal of Operational Research, Elsevier, vol. 280(1), pages 383-394.
    33. Eduardo Sánchez Ruenes & José Antonio Núñez Mora & Martha Beatriz Mota Aragón, 2020. "VaR and CVaR estimates in BRIC’s Oil Sector: A Normal Inverse Gaussian Distribution Approach," Economía: teoría y práctica, Universidad Autónoma Metropolitana, México, vol. 52(1), pages 207-236, Enero-Jun.
    34. Stefan Kassberger & Rüdiger Kiesel, 2006. "A fully parametric approach to return modelling and risk management of hedge funds," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 20(4), pages 472-491, December.
    35. Yiing Fei Tan & Kok Haur Ng & You Beng Koh & Shelton Peiris, 2022. "Modelling Trade Durations Using Dynamic Logarithmic Component ACD Model with Extended Generalised Inverse Gaussian Distribution," Mathematics, MDPI, vol. 10(10), pages 1-20, May.
    36. José Antonio Núñez & Mario I Contreras-Valdez & Carlos A Franco-Ruiz, 2019. "Statistical analysis of bitcoin during explosive behavior periods," PLOS ONE, Public Library of Science, vol. 14(3), pages 1-22, March.
    37. Frédéric Godin & Silvia Mayoral & Manuel Morales, 2012. "Contingent Claim Pricing Using a Normal Inverse Gaussian Probability Distortion Operator," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 79(3), pages 841-866, September.
    38. Vilar-Zanón, José L. & Lozano-Colomer, Cristina, 2007. "On Pareto Conjugate Priors and Their Application to Large Claims Reinsurance Premium Calculation," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 405-428, November.
    39. Virginie Konlack Socgnia & Diane Wilcox, 2014. "A Comparison of Generalized Hyperbolic Distribution Models for Equity Returns," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-15, June.
    40. Masafumi Nakano & Akihiko Takahashi & Soichiro Takahashi, 2019. "State Space Approach to Adaptive Fuzzy Modeling for Financial Investment," CIRJE F-Series CIRJE-F-1120, CIRJE, Faculty of Economics, University of Tokyo.
    Full references (including those not matched with items on IDEAS)

    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. Catania, Leopoldo & Grassi, Stefano, 2022. "Forecasting cryptocurrency volatility," International Journal of Forecasting, Elsevier, vol. 38(3), pages 878-894.
    2. Trojan, Sebastian, 2013. "Regime Switching Stochastic Volatility with Skew, Fat Tails and Leverage using Returns and Realized Volatility Contemporaneously," Economics Working Paper Series 1341, University of St. Gallen, School of Economics and Political Science, revised Aug 2014.
    3. Zdeněk Zmeškal & Dana Dluhošová & Karolina Lisztwanová & Antonín Pončík & Iveta Ratmanová, 2023. "Distribution Prediction of Decomposed Relative EVA Measure with Levy-Driven Mean-Reversion Processes: The Case of an Automotive Sector of a Small Open Economy," Forecasting, MDPI, vol. 5(2), pages 1-19, May.
    4. Roman V. Ivanov, 2023. "The Semi-Hyperbolic Distribution and Its Applications," Stats, MDPI, vol. 6(4), pages 1-21, October.
    5. Takahashi, Makoto & Watanabe, Toshiaki & Omori, Yasuhiro, 2016. "Volatility and quantile forecasts by realized stochastic volatility models with generalized hyperbolic distribution," International Journal of Forecasting, Elsevier, vol. 32(2), pages 437-457.
    6. BenSaïda, Ahmed & Slim, Skander, 2016. "Highly flexible distributions to fit multiple frequency financial returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 203-213.
    7. Jondeau, Eric, 2016. "Asymmetry in tail dependence in equity portfolios," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 351-368.
    8. Karlsson, Sune & Mazur, Stepan & Nguyen, Hoang, 2023. "Vector autoregression models with skewness and heavy tails," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    9. Deschamps, Philippe J., 2012. "Bayesian estimation of generalized hyperbolic skewed student GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3035-3054.
    10. Arismendi, Juan C. & Broda, Simon, 2017. "Multivariate elliptical truncated moments," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 29-44.
    11. Leovardo Mata Mata & José Antonio Núñez Mora & Ramona Serrano Bautista, 2021. "Multivariate Distribution in the Stock Markets of Brazil, Russia, India, and China," SAGE Open, , vol. 11(2), pages 21582440211, April.
    12. repec:cte:wsrepe:24552 is not listed on IDEAS
    13. Budhi Surya & Ryan Kurniawan, 2014. "Optimal Portfolio Selection Based on Expected Shortfall Under Generalized Hyperbolic Distribution," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(3), pages 193-236, September.
    14. 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.
    15. Wang, Chou-Wen & Liu, Kai & Li, Bin & Tan, Ken Seng, 2022. "Portfolio optimization under multivariate affine generalized hyperbolic distributions," International Review of Economics & Finance, Elsevier, vol. 80(C), pages 49-66.
    16. Sung Ik Kim, 2022. "ARMA–GARCH model with fractional generalized hyperbolic innovations," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-25, December.
    17. Hasanjan Sayit, 2022. "A discussion of stochastic dominance and mean-risk optimal portfolio problems based on mean-variance-mixture models," Papers 2202.02488, arXiv.org, revised Dec 2024.
    18. Masafumi Nakano & Akihiko Takahashi & Soichiro Takahashi, 2017. "Creating Investment Scheme with State Space Modeling ," CIRJE F-Series CIRJE-F-1038, CIRJE, Faculty of Economics, University of Tokyo.
    19. Thanakorn Nitithumbundit & Jennifer S. K. Chan, 2020. "ECM Algorithm for Auto-Regressive Multivariate Skewed Variance Gamma Model with Unbounded Density," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1169-1191, September.
    20. Marco Bee & Maria Michela Dickson & Flavio Santi, 2018. "Likelihood-based risk estimation for variance-gamma models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(1), pages 69-89, March.
    21. Laura Garcia-Jorcano & Alfonso Novales, 2020. "A dominance approach for comparing the performance of VaR forecasting models," Computational Statistics, Springer, vol. 35(3), pages 1411-1448, September.

    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:kap:compec:v:64:y:2024:i:1:d:10.1007_s10614-023-10457-5. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.