The Valuation of Options on Capacity

Options contracts can provide trading partners with enhanced flexibility to respond to uncertain market conditions and allow for superior capacity planning thanks to early information on future demand. We develop an analytical framework to value options on capacity for production of non-storable goods or dated services. The market set-up is as follows: During the contract market, period 0, the seller as the von Stackelberg leader announces a two-part tariff (r, e), consisting of an immediately payable reservation fee r and an execution fee e, due in the event the option is executed in period 1. The buyer in turn decides on how many options Q to purchase. Decisions are made under uncertainty: The buyer’s future demand, the seller’s future marginal costs as well as the future spot price are uncertain, the latter being impacted neither by the buyer nor the seller. During the spot market session, i.e., in period 1, the buyer may execute his options or satisfy his entire or additional demand from a competing seller in the spot market. The seller allocates reserved capacity now being called and attempts to sell remaining capacity into the spot market. Analytical expressions for the buyer’s optimal reservation quantity and the seller’s optimal tariff are derived, making explicit the risk-sharing benefits of options contracts accruing to both buyer and seller. The combination of an options contract and a spot market is demonstrated to be Pareto improving as compared to alternative market schemes. An analysis of the determinants of the efficiency gain characterizes industries particularly suitable to the options approach.