IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v22y2020i3d10.1007_s11009-019-09762-0.html
   My bibliography  Save this article

ECM Algorithm for Auto-Regressive Multivariate Skewed Variance Gamma Model with Unbounded Density

Author

Listed:
  • Thanakorn Nitithumbundit

    (University of Sydney)

  • Jennifer S. K. Chan

    (University of Sydney)

Abstract

The multivariate skewed variance gamma (MSVG) distribution is useful in modelling data with high density around the location parameter along with moderate heavy-tailedness. However, the density can be unbounded for certain choices of shape parameter. We propose a modification to the expectation-conditional maximisation (ECM) algorithm to calculate the maximum likelihood estimate (MLE) by introducing a small region to cap the conditional expectations in order to deal with the unbounded density. To facilitate application to financial time series, the mean is further extended to include autoregressive terms. Finally, the MSVG model is applied to analyse the returns of five daily closing price market indices. Standard error (SE) for the estimated parameters are computed using Louis’ method.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:3:d:10.1007_s11009-019-09762-0
    DOI: 10.1007/s11009-019-09762-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-019-09762-0
    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/s11009-019-09762-0?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. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Xiao‐Li Meng & David Van Dyk, 1997. "The EM Algorithm—an Old Folk‐song Sung to a Fast New Tune," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(3), pages 511-567.
    3. 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.
    4. Richard Finlay & Eugene Seneta, 2008. "Stationary‐Increment Variance‐Gamma and t Models: Simulation and Parameter Estimation," International Statistical Review, International Statistical Institute, vol. 76(2), pages 167-186, August.
    5. 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.
    6. Chou, Ray Yeutien, 2005. "Forecasting Financial Volatilities with Extreme Values: The Conditional Autoregressive Range (CARR) Model," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(3), pages 561-582, June.
    7. Shao, Xi-Dong & Lian, Yu-Jun & Yin, Lian-Qian, 2009. "Forecasting Value-at-Risk using high frequency data: The realized range model," Global Finance Journal, Elsevier, vol. 20(2), pages 128-136.
    8. Krzysztof Podgórski & Jonas Wallin, 2015. "Maximizing leave-one-out likelihood for the location parameter of unbounded densities," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 19-38, February.
    9. S.T. Boris Choy & Cathy W.S. Chen & Edward M.H. Lin, 2014. "Bivariate asymmetric GARCH models with heavy tails and dynamic conditional correlations," Quantitative Finance, Taylor & Francis Journals, vol. 14(7), pages 1297-1313, July.
    10. 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)

    Citations

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


    Cited by:

    1. Guney, Yesim & Arslan, Olcay & Yavuz, Fulya Gokalp, 2022. "Robust estimation in multivariate heteroscedastic regression models with autoregressive covariance structures using EM algorithm," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    2. 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.

    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. 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.
    2. Buchmann, Boris & Kaehler, Benjamin & Maller, Ross & Szimayer, Alexander, 2017. "Multivariate subordination using generalised Gamma convolutions with applications to Variance Gamma processes and option pricing," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2208-2242.
    3. Göncü, Ahmet & Karahan, Mehmet Oğuz & Kuzubaş, Tolga Umut, 2016. "A comparative goodness-of-fit analysis of distributions of some Lévy processes and Heston model to stock index returns," The North American Journal of Economics and Finance, Elsevier, vol. 36(C), pages 69-83.
    4. 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.
    5. Salem, Marwa Belhaj & Fouladirad, Mitra & Deloux, Estelle, 2022. "Variance Gamma process as degradation model for prognosis and imperfect maintenance of centrifugal pumps," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    6. Barsotti, Flavia & Viva, Luca Del, 2015. "Performance and determinants of the Merton structural model: Evidence from hedging coefficients," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 95-111.
    7. Gian P. Cervellera & Marco P. Tucci, 2017. "A note on the Estimation of a Gamma-Variance Process: Learning from a Failure," Computational Economics, Springer;Society for Computational Economics, vol. 49(3), pages 363-385, March.
    8. Boris Buchmann & Kevin W. Lu & Dilip B. Madan, 2018. "Calibration for Weak Variance-Alpha-Gamma Processes," Papers 1801.08852, arXiv.org, revised Jul 2018.
    9. 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 Jul 2023.
    10. 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.
    11. 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.
    12. Thomas Fung & Eugene Seneta, 2010. "Modelling and Estimation for Bivariate Financial Returns," International Statistical Review, International Statistical Institute, vol. 78(1), pages 117-133, April.
    13. 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.
    14. 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.
    15. Roberto Marfè, 2012. "A generalized variance gamma process for financial applications," Quantitative Finance, Taylor & Francis Journals, vol. 12(1), pages 75-87, June.
    16. Yeap, Claudia & Kwok, Simon S. & Choy, S. T. Boris, 2016. "A Flexible Generalised Hyperbolic Option Pricing Model and its Special Cases," Working Papers 2016-14, University of Sydney, School of Economics.
    17. Dilip B. Madan & Wim Schoutens & King Wang, 2017. "Measuring And Monitoring The Efficiency Of Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-32, December.
    18. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Center for Research in Economics and Statistics.
    19. Martijn Pistorius & Johannes Stolte, 2012. "Fast computation of vanilla prices in time-changed models and implied volatilities using rational approximations," Papers 1203.6899, arXiv.org.
    20. Björn Lutz, 2010. "Pricing of Derivatives on Mean-Reverting Assets," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-02909-7, October.

    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:spr:metcap:v:22:y:2020:i:3:d:10.1007_s11009-019-09762-0. 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.