Price level risk management in the presence of commodity options: income distribution, optimal market positions, and institutional value

Optimal risk management behavior is studied for decision makers who wish to manage price level risk with commodity futures and options contracts. The income distribution that results when both futures and put options are held in a risk management portfolio is derived for the case of a known end-of-period output level. The resulting income distribution is the sum of two truncated normal distributions and violates the sufficient condition that causes the linear mean-variance model to produce results which are consistent with expected utility maximization. Numerical integration and numerical optimization methods are developed to solve the expected utility maximization problem. The optimal market positions are found for a predetermined set of market characteristics in both the mean-variance and expected utility maximization problem. The optimal market positions are found for a predetermined set of market characteristics in both the mean-variance and expected utility frameworks for the case of a certain end-of-period output level;The relationship between the expected utility market positions and the relevant market factors are estimated using a polynomial function. Localized comparative static results are generated using the numerical solution methods. The results show that the decision maker will hedge his/her end-of-period output in the futures market using the traditional one-to-one hedge and then speculate in both markets if either market is believed to be biased. The value of using the expected utility solutions instead of the solutions produced by the mean-variance or polynomial approximation models is shown to be quite small for the levels of market factors considered in the study. If both the futures and put options markets are unbiased, there is no value in adding a put options market when a futures market currently exists. If a bias exists in either market, there is value in adding a put options market when a futures market currently exists, although the value is relatively small.