Option Contracts in Supply Chains∗

This article investigates the pricing of options when the demand curve is downward sloping. Our speciÞc application arises in a supply chain setting, where a manufacturer offers the retailer the right to reorder items at a Þxed price and/or the right to return unsold goods for a predetermined salvage value. We show that the introduction of option contracts causes the wholesale price to increase and the volatility of the retail price to decrease. Conditions are derived under which the manufacturer is always better off by introducing options. In general, options are not zero sum games. In some cases the retailer also beneÞts while in other cases the retailer is worse off. If the uncertainty in the demand curve is sufficiently high, the introduction of option contracts alters the equilibrium prices in a way that hurts the retailer. Finally, we demonstrate that if either the manufacturer or the retailer wants to hedge the risk, contracts that pay out according to the square of the price of a traded security are required. Many studies have been performed in industries such as apparel, sporting goods and toys, where there are long lead times, short selling seasons and high demand uncertainties. For these problems one avenue of research is concerned with the design of contracting relationships that provide retailers with ßexibility in responding to unanticipated demand and prices over the sales season. This paper examines such contracting arrangements in a supply chain setting consisting of an upstream party (which we refer to as the manufacturer) whose only access to the product market is via a single downstream party (which we refer to as the retailer). To manage the risk of inventories associated with uncertain demand, it is fairly common for the manufacturer to provide the retailer with an array of products, including reordering contracts, or call options, that allow the retailer to purchase additional goods at a predetermined time for a Þxed price, and return contracts, or put options, that allow the retailer to return unsold goods at a predetermined salvage price. By purchasing inventory, together with a portfolio of these supply chain call and put options, the retailer has more choices that allows a strategy to be put into place to best meets its interests. The manufacturer’s goal is to design the terms of the reordering and return option contracts and establish their prices, together with the wholesale price, so as to induce the retailer to take optimal actions that best serve the manufacturer’s interests.1 By introducing reorder and return option contracts, the manufacturer alters the retailer’s sequence of decisions. This in turn has a feedback effect in that the equilibrium wholesale and retail prices are affected. In this paper we are particularly interested in how these prices adjust after the introduction of supply chain options. We are also interested in establishing the pricing mechanism that the manufacturer uses for the supply chain options. Indeed, our problem environment is set up so that we can closely examine the pricing of option contracts in a downward sloping demand curve environment. Moreover, since we assume that there are sufficient Þnancial products that span all uncertainty, we are able to unambiguously value the beneÞt of the supply chain options without explicitly incorporating risk aversion factors. The usual approach in pricing real options follows the Black-Scholes (1973) andMerton (1974) paradigm, in which contracts are replicated by dynamic self Þnancing trading schemes in the underlying asset and in riskless bonds. In this approach, derivative contracts are redundant and do not affect prices of assets in the marketplace. In order to investigate how derivative contracts might impact prices, it is necessary to move away from the typical partial equilibrium arbitrage free paradigm and to allow for the possibility that these claims have feedback effects that may alter equilibrium prices of the underlying assets. In the Þnancial options literature, there is a large number of studies that have investiThe existence of multiple decision makers with different ownership interests results in departures from Þrstbest solutions and creates strong incentives for parties to enter into contracts that enhance system-wide performance and improve channel coordination.