Statistical properties of derivatives: a journey in term structures

This article presents an empirical study of thirteen derivative markets for commodity and financial assets. This paper goes beyond statistical analysis by including the maturity as a variable for futures contracts’s daily returns, 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 of 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, reminding of a phase diagram with a sharp transition at the 18th delivery month.