Optimal Hedging and Equilibrium in a Dynamic Futures Market

In this paper optimal hedging strategies are solved for in a continuous time setting. We consider a single agent maximizing the expected utility of the sum of the terminal value of a fixed portfolio of spot market assets and the terminal value of a margin account on a futures trading position. Closed form solutions for the optimal hedging strategy are provided for general “smooth” utility functions under the expectations hypothesis, and for exponential Von Neumann-Morgenstern utility (without the expectations hypothesis). Necessary conditions for an equilibrium are shown. Finally, the optimal hedge is provided for log-normal spot price distributions, assuming the prices of the futures are the expected prices of the spot assets at delivery.