IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1810.01116.html
   My bibliography  Save this paper

Inverse Gaussian quadrature and finite normal-mixture approximation of the generalized hyperbolic distribution

Author

Listed:
  • Jaehyuk Choi
  • Yeda Du
  • Qingshuo Song

Abstract

In this study, a numerical quadrature for the generalized inverse Gaussian distribution is derived from the Gauss-Hermite quadrature by exploiting its relationship with the normal distribution. The proposed quadrature is not Gaussian, but it exactly integrates the polynomials of both positive and negative orders. Using the quadrature, the generalized hyperbolic distribution is efficiently approximated as a finite normal variance-mean mixture. Therefore, the expectations under the distribution, such as cumulative distribution function and European option price, are accurately computed as weighted sums of those under normal distributions. The generalized hyperbolic random variates are also sampled in a straightforward manner. The accuracy of the methods is illustrated with numerical examples.

Suggested Citation

  • Jaehyuk Choi & Yeda Du & Qingshuo Song, 2018. "Inverse Gaussian quadrature and finite normal-mixture approximation of the generalized hyperbolic distribution," Papers 1810.01116, arXiv.org, revised Dec 2020.
    • Handle: RePEc:arx:papers:1810.01116
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1810.01116
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Karlis, Dimitris, 2002. "An EM type algorithm for maximum likelihood estimation of the normal-inverse Gaussian distribution," Statistics & Probability Letters, Elsevier, vol. 57(1), pages 43-52, March.
    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. Taufer, Emanuele & Leonenko, Nikolai, 2009. "Simulation of Lvy-driven Ornstein-Uhlenbeck processes with given marginal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2427-2437, April.
    2. Shaw, Charles, 2018. "Regime-Switching And Levy Jump Dynamics In Option-Adjusted Spreads," MPRA Paper 94154, University Library of Munich, Germany, revised 27 May 2019.
    3. Fischer, Thomas & Lundtofte, Frederik, 2020. "Unequal returns: Using the Atkinson index to measure financial risk," Journal of Banking & Finance, Elsevier, vol. 116(C).
    4. Boudt, Kris & Raza, Muhammad Wajid & Wauters, Marjan, 2019. "Evaluating the Shariah-compliance of equity portfolios: The weighting method matters," International Review of Financial Analysis, Elsevier, vol. 63(C), pages 406-417.
    5. Iván Blanco, Juan Ignacio Peña, and Rosa Rodriguez, 2018. "Modelling Electricity Swaps with Stochastic Forward Premium Models," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2).
    6. F. Godin, 2016. "Minimizing CVaR in global dynamic hedging with transaction costs," Quantitative Finance, Taylor & Francis Journals, vol. 16(3), pages 461-475, March.
    7. Boudt, Kris & Cornilly, Dries & Verdonck, Tim, 2020. "Nearest comoment estimation with unobserved factors," Journal of Econometrics, Elsevier, vol. 217(2), pages 381-397.
    8. Weron, Rafał, 2004. "Computationally intensive Value at Risk calculations," Papers 2004,32, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    9. Zhou, Shirong & Tang, Yincai & Xu, Ancha, 2021. "A generalized Wiener process with dependent degradation rate and volatility and time-varying mean-to-variance ratio," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    10. S. Ghasemzadeh & M. Ganjali & T. Baghfalaki, 2022. "Quantile regression via the EM algorithm for joint modeling of mixed discrete and continuous data based on Gaussian copula," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(5), pages 1181-1202, December.
    11. Chen, Ying & Niu, Linlin & Chen, Ray-Bing & He, Qiang, 2019. "Sparse-Group Independent Component Analysis with application to yield curves prediction," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 76-89.
    12. 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.
    13. 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.
    14. Lillestøl, Jostein, 2007. "Some new bivariate IG and NIG-distributions for modelling covariate nancial returns," Discussion Papers 2007/1, Norwegian School of Economics, Department of Business and Management Science.
    15. Borak, Szymon & Misiorek, Adam & Weron, Rafał, 2010. "Models for heavy-tailed asset returns," SFB 649 Discussion Papers 2010-049, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    16. Xiaoping Zhou & Dmitry Malioutov & Frank J. Fabozzi & Svetlozar T. Rachev, 2014. "Smooth monotone covariance for elliptical distributions and applications in finance," Quantitative Finance, Taylor & Francis Journals, vol. 14(9), pages 1555-1571, September.
    17. Zhao, Kaifeng & Lian, Heng, 2016. "The Expectation–Maximization approach for Bayesian quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 1-11.
    18. 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.
    19. Yang Minxian, 2011. "Volatility Feedback and Risk Premium in GARCH Models with Generalized Hyperbolic Distributions," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(3), pages 1-21, May.
    20. Wen-Liang Hung & Shou-Jen Chang-Chien, 2017. "Learning-based EM algorithm for normal-inverse Gaussian mixture model with application to extrasolar planets," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(6), pages 978-999, April.

    More about this item

    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:1810.01116. 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.