IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v390y2011i11p2009-2019.html
   My bibliography  Save this article

Statistical properties of derivatives: A journey in term structures

Author

Listed:
  • Lautier, Delphine
  • Raynaud, Franck

Abstract

This article presents an empirical study of 13 derivative markets for commodities and financial assets. The study goes beyond statistical analysis by including the maturity as a variable for the daily returns of futures contracts from 1998 to 2010, and for delivery dates up to 120 months. We observe that the mean and variance of the commodities follow a scaling behavior in the maturity dimension with an exponent characteristic of the Samuelson effect. The comparison between the tails of the probability distribution according to the expiration dates shows that there is a segmentation in the fat tails exponent term structure above the Lévy stable region. Finally, we compute the average tail exponent for each maturity, and we observe two regimes of extreme events for derivative markets, reminiscent of a phase diagram with a sharp transition at the 18th delivery month.

Suggested Citation

  • Lautier, Delphine & Raynaud, Franck, 2011. "Statistical properties of derivatives: A journey in term structures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 2009-2019.
  • Handle: RePEc:eee:phsmap:v:390:y:2011:i:11:p:2009-2019
    DOI: 10.1016/j.physa.2011.01.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437111000823
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    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. Angus Deaton & Guy Laroque, 1992. "On the Behaviour of Commodity Prices," Review of Economic Studies, Oxford University Press, vol. 59(1), pages 1-23.
    2. Parameswaran Gopikrishnan & Vasiliki Plerou & Luis A. Nunes Amaral & Martin Meyer & H. Eugene Stanley, 1999. "Scaling of the distribution of fluctuations of financial market indices," Papers cond-mat/9905305, arXiv.org.
    3. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    4. M. Bartolozzi & C. Mellen & T. Di Matteo & T. Aste, 2007. "Multi-scale correlations in different futures markets," Papers 0707.3321, arXiv.org, revised Aug 2007.
    5. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
    6. Bertrand M. Roehner, 1996. "The Role of Transportation Costs in the Economics of Commodity Markets," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 78(2), pages 339-353.
    7. Brennan, Michael J & Schwartz, Eduardo S, 1985. "Evaluating Natural Resource Investments," The Journal of Business, University of Chicago Press, vol. 58(2), pages 135-157, April.
    8. Chambers, Marcus J & Bailey, Roy E, 1996. "A Theory of Commodity Price Fluctuations," Journal of Political Economy, University of Chicago Press, vol. 104(5), pages 924-957, October.
    9. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    10. Cortazar, Gonzalo & Schwartz, Eduardo S., 2003. "Implementing a stochastic model for oil futures prices," Energy Economics, Elsevier, vol. 25(3), pages 215-238, May.
    11. repec:dau:papers:123456789/95 is not listed on IDEAS
    12. M. Bartolozzi & C. Mellen & T. Di Matteo & T. Aste, 2007. "Multi-scale correlations in different futures markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 58(2), pages 207-220, July.
    13. Clementi, F. & Di Matteo, T. & Gallegati, M., 2006. "The power-law tail exponent of income distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 49-53.
    14. Tabak, Benjamin M. & Cajueiro, Daniel O., 2005. "The long-range dependence behavior of the term structure of interest rates in Japan," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 418-426.
    15. Cajueiro, Daniel O. & Tabak, Benjamin M., 2007. "Long-range dependence and multifractality in the term structure of LIBOR interest rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 603-614.
    16. Schwartz, Eduardo S, 1997. " The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-973, July.
    17. Parameswaran Gopikrishnan & Martin Meyer & Luis A Nunes Amaral & H Eugene Stanley, 1998. "Inverse Cubic Law for the Probability Distribution of Stock Price Variations," Papers cond-mat/9803374, arXiv.org, revised May 1998.
    18. Fama, Eugene F & French, Kenneth R, 1987. "Commodity Futures Prices: Some Evidence on Forecast Power, Premiums,and the Theory of Storage," The Journal of Business, University of Chicago Press, vol. 60(1), pages 55-73, January.
    19. Gu, Gao-Feng & Chen, Wei & Zhou, Wei-Xing, 2008. "Empirical distributions of Chinese stock returns at different microscopic timescales," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 495-502.
    20. G.-H. Mu & W. Chen & J. Kertész & W.-X. Zhou, 2009. "Preferred numbers and the distributions of trade sizes and trading volumes in the Chinese stock market," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 68(1), pages 145-152, 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. repec:dau:papers:123456789/13630 is not listed on IDEAS
    2. García-Carranco, Sergio M. & Bory-Reyes, Juan & Balankin, Alexander S., 2016. "The crude oil price bubbling and universal scaling dynamics of price volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 60-68.
    3. Edouard Jaeck & Delphine Lautier, 2014. "Samuelson hypothesis and electricity derivative markets," Post-Print hal-01655800, HAL.
    4. repec:dau:papers:123456789/14413 is not listed on IDEAS
    5. Jaeck, Edouard & Lautier, Delphine, 2016. "Volatility in electricity derivative markets: The Samuelson effect revisited," Energy Economics, Elsevier, vol. 59(C), pages 300-313.

    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:eee:phsmap:v:390:y:2011:i:11:p:2009-2019. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.