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Statistical properties of derivatives: a journey in term structures


  • Delphine Lautier
  • Franck Raynaud


This article presents an empirical study of thirteen derivative markets for commodity and financial assets. It compares the statistical properties of futures contracts's daily returns at different maturities, from 1998 to 2010 and for delivery dates up to 120 months. The analysis of the fourth first moments of the distribution shows that the mean and variance of the commodities follow a scaling behavior in the maturity dimension. The comparison of the tails of the probability distribution according to the expiration dates also shows that there is a segmentation in the fat tails exponent term structure above the L'evy stable region. Finally, the test of the robustness of the inverse cubic law in the maturity dimension shows that there are two regimes of extreme events for derivative markets, reminding of a phase diagram with a transition value at the 18th delivery month.

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  • Delphine Lautier & Franck Raynaud, 2010. "Statistical properties of derivatives: a journey in term structures," Papers 1010.6026,
  • Handle: RePEc:arx:papers:1010.6026

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    References listed on IDEAS

    1. Giovanni Di Masi & Tomas Björk & Wolfgang Runggaldier & Yuri Kabanov, 1997. "Towards a general theory of bond markets (*)," Finance and Stochastics, Springer, vol. 1(2), pages 141-174.
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    Cited by:

    1. Edouard Jaeck & Delphine Lautier, 2014. "Samuelson hypothesis and electricity derivative markets," Post-Print hal-01655800, HAL.
    2. repec:dau:papers:123456789/13630 is not listed on IDEAS
    3. Pierre-Arnaud Drouhin & Arnaud Simon & Yasmine Essafi, 2016. "Forward Curve Risk Factors Analysis in the UK Real Estate Market," The Journal of Real Estate Finance and Economics, Springer, vol. 53(4), pages 494-526, November.

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