  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.

Statistical Finance