Recommended Paper – Commodities Futures Curves

A paper (PDF) written back in 1991 by Jacques Gabillon is an excellent introduction to futures curves. He describes the general features of futures curves and specifically those in the oil market, such as the typical ways they change over time, the concepts of ‘backwardation’ and ‘contango’, and the term structure of volatility. He compares the futures curve with the term structure of interest rates.

He then goes on to examine simple models for oil prices using a single SDE (stochastic differential equation) to describe the short-term movements, and clearly explains the role of convenience yield and why cannot be a constant in time and across all maturities. He gradually adds necessary features to a simple oil model to captures more and more empirically observed features of the futures curve. This culminates in his proposed 2-factor model, now known as the Gabillon Model, having both the short term and (unobserved) long term price of oil represented as an (arithmetic) Brownian Motion.

As well as an excellent introduction to his own model, Gabillon’s paper (freely available here (PDF), no login required) is a great introduction to futures curves. It is as relevant today as when it was written, and the principles apply to all commodities, not just oil.


Gabillon, J. 1991. The term structures of oil futures prices. Working Paper. Oxford Institute for Energy Studies.

3 Responses to Recommended Paper – Commodities Futures Curves

  1. peregrinecap says:

    I like your homepage. Thanks.
    Keep it up.

  2. Neelesh says:

    Excellent blog and resources…thanks a lot.

    regarding the link to the classic paper from Gabillon the new URL is

    Click to access WPM17-TheTermStructureofOilFuturesPrices-JGabillon-1991.pdf

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