IDEAS home Printed from https://ideas.repec.org/a/taf/oaefxx/v5y2017i1p1318813.html
   My bibliography  Save this article

Parameter estimation for stable distributions with application to commodity futures log-returns

Author

Listed:
  • M. Kateregga
  • S. Mataramvura
  • D. Taylor

Abstract

This paper explores the theory behind the rich and robust family of α$ \alpha $-stable distributions to estimate parameters from financial asset log-returns data. We discuss four-parameter estimation methods including the quantiles, logarithmic moments method, maximum likelihood (ML), and the empirical characteristics function (ECF) method. The contribution of the paper is two-fold: first, we discuss the above parametric approaches and investigate their performance through error analysis. Moreover, we argue that the ECF performs better than the ML over a wide range of shape parameter values, α$ \alpha $ including values closest to 0 and 2 and that the ECF has a better convergence rate than the ML. Secondly, we compare the t location-scale distribution to the general stable distribution and show that the former fails to capture skewness which might exist in the data. This is observed through applying the ECF to commodity futures log-returns data to obtain the skewness parameter.

Suggested Citation

  • M. Kateregga & S. Mataramvura & D. Taylor, 2017. "Parameter estimation for stable distributions with application to commodity futures log-returns," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1318813-131, January.
  • Handle: RePEc:taf:oaefxx:v:5:y:2017:i:1:p:1318813
    DOI: 10.1080/23322039.2017.1318813
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/23322039.2017.1318813
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/23322039.2017.1318813?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. Benoit Mandelbrot, 1962. "Paretian Distributions and Income Maximization," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 76(1), pages 57-85.
    2. Jun Yu, 2004. "Empirical Characteristic Function Estimation and Its Applications," Econometric Reviews, Taylor & Francis Journals, vol. 23(2), pages 93-123.
    3. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    4. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420-420.
    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. M. Kateregga & S. Mataramvura & D. Taylor & Xibin Zhang, 2017. "Bismut–Elworthy–Li formula for subordinated Brownian motion applied to hedging financial derivatives," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1384125-138, January.
    2. Abootaleb Shirvani & Svetlozar T. Rachev & Frank J. Fabozzi, 2019. "Multiple Subordinated Modeling of Asset Returns," Papers 1907.12600, arXiv.org.
    3. Bielak, Łukasz & Grzesiek, Aleksandra & Janczura, Joanna & Wyłomańska, Agnieszka, 2021. "Market risk factors analysis for an international mining company. Multi-dimensional, heavy-tailed-based modelling," Resources Policy, Elsevier, vol. 74(C).
    4. Taurai Muvunza, 2020. "An $\alpha$-Stable Approach to Modelling Highly Speculative Assets and Cryptocurrencies," Papers 2002.09881, arXiv.org, revised Jul 2023.

    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. Michael Kateregga & Sure Mataramvura & David Taylor, 2017. "Parameter estimation for stable distributions with application to commodity futures log returns," Papers 1706.09756, arXiv.org.
    2. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    3. Hayley Jang & Young Hoon Lee & Rodney Fort, 2019. "Winning In Professional Team Sports: Historical Moments," Economic Inquiry, Western Economic Association International, vol. 57(1), pages 103-120, January.
    4. 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.
    5. Alexander Eastman & Brian Lucey, 2008. "Skewness and asymmetry in futures returns and volumes," Applied Financial Economics, Taylor & Francis Journals, vol. 18(10), pages 777-800.
    6. Ortobelli, Sergio & Rachev, Svetlozar & Schwartz, Eduardo, 2000. "The Problem of Optimal Asset Allocation with Stable Distributed Returns," University of California at Los Angeles, Anderson Graduate School of Management qt3zd6q86c, Anderson Graduate School of Management, UCLA.
    7. Fergusson, Kevin, 2020. "Less-Expensive Valuation And Reserving Of Long-Dated Variable Annuities When Interest Rates And Mortality Rates Are Stochastic," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 381-417, May.
    8. 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.
    9. Stoyan Stoyanov & Borjana Racheva-Iotova & Svetlozar Rachev & Frank Fabozzi, 2010. "Stochastic models for risk estimation in volatile markets: a survey," Annals of Operations Research, Springer, vol. 176(1), pages 293-309, April.
    10. repec:uts:finphd:40 is not listed on IDEAS
    11. Rashid, Abdul, 2007. "Stock prices and trading volume: An assessment for linear and nonlinear Granger causality," Journal of Asian Economics, Elsevier, vol. 18(4), pages 595-612, August.
    12. Einmahl, John & He, Y., 2020. "Unified Extreme Value Estimation for Heterogeneous Data," Other publications TiSEM dfe6c38c-823b-4394-b4fd-a, Tilburg University, School of Economics and Management.
    13. Zaevski, Tsvetelin S. & Kim, Young Shin & Fabozzi, Frank J., 2014. "Option pricing under stochastic volatility and tempered stable Lévy jumps," International Review of Financial Analysis, Elsevier, vol. 31(C), pages 101-108.
    14. Pernagallo, Giuseppe & Torrisi, Benedetto, 2020. "Blindfolded monkeys or financial analysts: Who is worth your money? New evidence on informational inefficiencies in the U.S. stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    15. Anand, Abhinav & Li, Tiantian & Kurosaki, Tetsuo & Kim, Young Shin, 2016. "Foster–Hart optimal portfolios," Journal of Banking & Finance, Elsevier, vol. 68(C), pages 117-130.
    16. Yoshio Miyahara & Alexander Novikov, 2001. "Geometric Lévy Process Pricing Model," Research Paper Series 66, Quantitative Finance Research Centre, University of Technology, Sydney.
    17. Sabiou M. Inoua & Vernon L. Smith, 2022. "Perishable goods versus re-tradable assets: A theoretical reappraisal of a fundamental dichotomy," Chapters, in: Sascha Füllbrunn & Ernan Haruvy (ed.), Handbook of Experimental Finance, chapter 15, pages 162-171, Edward Elgar Publishing.
    18. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    19. Ergun, Lerby M., 2016. "Disaster and fortune risk in asset returns," LSE Research Online Documents on Economics 66194, London School of Economics and Political Science, LSE Library.
    20. David Allen & Stephen Satchell & Colin Lizieri, 2024. "Quantifying the non-Gaussian gain," Journal of Asset Management, Palgrave Macmillan, vol. 25(1), pages 1-18, February.
    21. Bryan Kelly & Hao Jiang, 2013. "Tail Risk and Asset Prices," NBER Working Papers 19375, National Bureau of Economic Research, Inc.

    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:taf:oaefxx:v:5:y:2017:i:1:p:1318813. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/OAEF20 .

    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.