The impact of delivery risk on optimal production and futures hedging

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. This imposes an additional delivery risk on hedgers. This paper derives the optimal production and futures hedging strategy for a risk-averse competitive firm in the presence of delivery risk. We show that, depending on its relative valuation, the delivery option may induce the firm to produce more than in the absence of delivery risk. If delivery risk is additively related to commodity price risk, the firm will under-hedge its exposure to commodity price risk. If delivery risk is multiplicatively related to commodity price risk, the firm will under- or over-hedge this exposure. For constant relative risk aversion, this is illustrated by a numerical example.