Newsvendor Model as an Exchange Option on Demand and Supply Uncertainty

Using a contingent claims framework, we develop a single period model in the context of an exchange option in a discounted value maximization setting. Given this framework, we study the classic problem of determining stockpiling levels prior to demand realization when the procured/produced levels are subject to random yield variations. In this set up, both demand and yield variables are modeled as Wiener processes. A pure noise (zero drift) process initially models yield dynamics. Later, we consider improving the average yield rates, subsidized through increasing unit costs in a constrained cost environment. In either case, "yield adjusted" critical fractiles, the optimal order/production levels, and their corresponding expected values are established. As a special case, we relax the yield uncertainty constraint and instead use the long-term average yield estimate to assess the yield's impact on production/procurement levels. In this context, we establish that the above results collapse to the well-known Black-Scholes/Merton (1973) option-pricing model. Given the original framework of this study, we show the counterintuitive results that unit profits, due to improved average yield rates, may actually decrease. We also demonstrate that a reliable metric to justify yield improvements is the relative net positive marginal unit profit. Our paper also provides detailed comparative statics, both analytically and numerically. These results provide useful insights into policy making by identifying operating regions where the expected marginal unit profits warrant yield improvement. The results provided can readily be generalized to other economic-based Newsvendor model parameters.