The optimal hedging portfolio is shown to include both futures and options under a variety of circumstances when the marginal cost of hedging is non-zero. Futures and options are treated as substitute goods, and properties of the resulting hedging demand system are explained. The overall optimal...

We derive a new hedge ratio based on weighted expected utility. Weighted expected utility is a generalization of expected utility that permits non-linear probability weights. Generally speaking weighted expected utility hedge ratios are less than minimum variance hedge ratios and larger than...