Optimal Hedging and Equilibrium in a Dynamic Futures Market*

This paper solves the optimal futures hedging problem in several simple continuous-time settings, and examines the resultant equilibrium in one case. Spot and futures prices are described by vector diffusion processes. A hedge is a vector stochastic process specifying a futures position in each futures market. Hedging profits and losses are marked to market in an interest-bearing (or interest-paying) margin account. A hedge is optimal if it maximizes the expected utility of terminal wealth, which is the market value of a committed portfolio of spot market assets plus the terminal value of the margin account. The special cases solved in this paper are quite restrictive. In particular, in all of the cases, futures prices are either martingales or have independent normally distributed price increments. In some cases, it has been difficult to empirically reject the martingale hypothesis for many contracts. [See, for example, Cornell (1977), Dusak (1973), Hansen and Hodrick (1980), and Jackson (1985).] Nevertheless, the martingale assumption is extremely restrictive from a theoretical point of view. The Gaussian price process assumption,