Multiple delivery specifications exist on nearly all commodity futures contracts. Sellers are typically allowed to choose among several grades of the underlying commodity. On the delivery day, the futures price converges to the spot price of the cheapest-to-deliver grade rather than to that of the par-delivery grade of the commodity, thereby imposing an additional delivery risk on hedgers. This paper derives the optimal production and futures hedging strategy for a risk-averse competitive firm facing delivery risk. We show that the option value of the multiple delivery specification induces the firm to produce more with than without the delivery risk if the firm gauges this value higher than the market. We further show that if the delivery risk is additively related to the commodity price risk, the firm optimally under-hedges its risk exposure. On the other hand, if the delivery risk is multiplicatively related to the commodity price risk, the firm may optimally choose an under- or over-hedge which we illustrate using a numerical example.

Cross hedging price risk in an incomplete financial market creates basis risk. We propose a new way of modeling basis risk where price risk and basis risk are combined in a multiplicative way. Under this specification, positive prudence is a necessary and sufficient condition for underhedging in an unbiased market. Using the example of cross hedging jet fuel price risk with crude oil futures, we show that the new specification is superior in describing the price series and that optimal cross hedges differ significantly from those derived under the traditional additive cross hedging model.