A Convenience Yield Approximation Model for Mean-Reverting Commodities

Standard option-based approximations for convenience yields make use of the assumption that commodity spot prices follow a geometric Brownian motion. While there is some empirical support for this assumption, prices of a wide variety of (agricultural) commodities mean revert. Using a mean-reverting spot price process we derive a novel convenience yield approximation analytically. It corresponds to the difference between the present values of two floating-strike Asian options written on the spot and the futures prices, respectively. Using natural gas spot and futures price data from four different trading locations, we compare convenience yield estimates derived from existing approximations to those of our new measure. We find that convenience yield estimates vary substantially across approximation methods and that differences can be attributed to the cost of carry and the moneyness of the options.