IDEAS home Printed from https://ideas.repec.org/p/hhs/nhhfms/2007_001.html

Some new bivariate IG and NIG-distributions for modelling covariate nancial returns

Author

Listed:
  • Lillestøl, Jostein

    (Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration)

Abstract

The univariate Normal Inverse Gaussian (NIG) distribution is found useful for modelling financial return data exhibiting skewness and fat tails. Multivariate versions exists, but may be impractical to implement in finance. This work explores some possibilities with links to the mixing representation of the NIG distribution by the IG-distribution. We present two approaches for constructing bivariate NIG distribution that take advantage of the correlation between the univariate latent IG-variables that characterizes the marginal NIG-distribution. These are readily available from the marginal estimation, either by maximum likelihood via the EM-algorithm or by Bayesian estimation via Markov chain Monte Carlo methods. A context for implementation in finance is given.

Suggested Citation

  • 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.
    • Handle: RePEc:hhs:nhhfms:2007_001
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/11250/163898
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Anders Eriksson & Lars Forsberg & Eric Ghysels, 2004. "Approximating the Probability Distribution of Functions of Random Variables: A New Approach," CIRANO Working Papers 2004s-21, CIRANO.
    2. Tina Hviid Rydberg, 2000. "Realistic Statistical Modelling of Financial Data," International Statistical Review, International Statistical Institute, vol. 68(3), pages 233-258, December.
    3. 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. 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.
    2. 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.
    3. Wang, Shangshan & Xiang, Liming, 2017. "Two-layer EM algorithm for ALD mixture regression models: A new solution to composite quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 136-154.
    4. Ciprian Necula & Gabriel Drimus & Walter Farkas, 2019. "A general closed form option pricing formula," Review of Derivatives Research, Springer, vol. 22(1), pages 1-40, April.
    5. Kei Katahira & Yu Chen & Gaku Hashimoto & Hiroshi Okuda, 2019. "Development of an agent-based speculation game for higher reproducibility of financial stylized facts," Papers 1902.02040, arXiv.org.
    6. Aur'elien Alfonsi & Nerea Vadillo, 2023. "Risk valuation of quanto derivatives on temperature and electricity," Papers 2310.07692, arXiv.org, revised Apr 2024.
    7. 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.
    8. Fischer, Thomas & Lundtofte, Frederik, 2020. "Unequal returns: Using the Atkinson index to measure financial risk," Journal of Banking & Finance, Elsevier, vol. 116(C).
    9. Zakamouline, Valeri & Koekebakker, Steen, 2009. "Portfolio performance evaluation with generalized Sharpe ratios: Beyond the mean and variance," Journal of Banking & Finance, Elsevier, vol. 33(7), pages 1242-1254, July.
    10. 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.
    11. Norbert Henze & María Dolores Jiménez-Gamero, 2019. "A new class of tests for multinormality with i.i.d. and garch data based on the empirical moment generating function," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 499-521, June.
    12. Aknouche, Abdelhakim & Almohaimeed, Bader & Dimitrakopoulos, Stefanos, 2024. "Noising the GARCH volatility: A random coefficient GARCH model," MPRA Paper 120456, University Library of Munich, Germany, revised 15 Mar 2024.
    13. Puzanova, Natalia & Siddiqui, Sikandar & Trede, Mark, 2009. "Approximate value-at-risk calculation for heterogeneous loan portfolios: Possible enhancements of the Basel II methodology," Journal of Financial Stability, Elsevier, vol. 5(4), pages 374-392, December.
    14. repec:aen:journl:ej39-2-pena is not listed on IDEAS
    15. Ankur Chakraborty & Nabakumar Jana, 2025. "Bayes estimation of ratio of scale-like parameters for inverse Gaussian distributions and applications to classification," Computational Statistics, Springer, vol. 40(5), pages 2249-2276, June.
    16. Katahira, Kei & Chen, Yu & Akiyama, Eizo, 2021. "Self-organized Speculation Game for the spontaneous emergence of financial stylized facts," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    17. F. Godin, 2016. "Minimizing CVaR in global dynamic hedging with transaction costs," Quantitative Finance, Taylor & Francis Journals, vol. 16(3), pages 461-475, March.
    18. Boudt, Kris & Cornilly, Dries & Verdonck, Tim, 2020. "Nearest comoment estimation with unobserved factors," Journal of Econometrics, Elsevier, vol. 217(2), pages 381-397.
    19. Maria P. Braun & Simos G. Meintanis & Viatcheslav B. Melas, 2008. "Optimal Design Approach to GMM Estimation of Parameters Based on Empirical Transforms," International Statistical Review, International Statistical Institute, vol. 76(3), pages 387-400, December.
    20. Weron, Rafał, 2004. "Computationally intensive Value at Risk calculations," Papers 2004,32, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    21. 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).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

    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:hhs:nhhfms:2007_001. 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: Stein Fossen (email available below). General contact details of provider: https://edirc.repec.org/data/dfnhhno.html .

    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.