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AbstractMultiple delivery speci cations 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 rm in the presence of delivery risk. We show that, depending on its relative valuation, the delivery option may induce the rm to produce more than in the absence of delivery risk. If delivery risk is additively related to commodity price risk, the rm will under-hedge its exposure to commodity price risk. If delivery risk is multiplicatively related to commodity price risk, the rm will under-or over-hedge this exposure. For constant relative risk aversion, this is illustrated by a numerical example.
JEL classi cation: G11, D81Keywords: delivery risk, futures, risk management, production * We gratefully acknowledge nancial support from the Germany/Hong Kong Joint Research Scheme provided by the German Academic Exchange Service (DAAD) and the Hong Kong Research Grants Council (RGC). We would like to thank Günter Franke and Donald Lien for very helpful comments and Harald Lohre for valuable research assistance. Remaining errors are our responsibility.
1The impact of delivery risk on optimal production and futures hedgingMultiple delivery speci cations 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 pardelivery 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 rm in the presence of delivery risk. We show that, depending on its relative valuation, the delivery option may induce the rm to produce more than in the absence of delivery risk. If delivery risk is additively related to commodity price risk, the rm will under-hedge its exposure to commodity price risk. If delivery risk is multiplicatively related to commodity price risk, the rm will under-or over-hedge this exposure. For constant relative risk aver...