In a supply chain, a retailer could transfer demand uncertainty to its supplier by signing a supply contract, requiring the supplier to prepare more inventories to meet the retailer’s needs. When the retailer has a right to lock in the wholesale price via the supply contract, it owns a real option in the supply contract. In most cases, the predetermined price in the supply contract only comprises the supplier’s unit cost and unit margin profit. Real option value is often neglected.
As a result, wholesale price is undervalued. This paper aims to address the pricing problem by using a correlated stochastic model. We assume that the market demands are correlated in time horizons. There exist two echelons in the supply chain: the business market and the consumer market. The demands in the consumer market are assumed to follow a fractional Brownian motion. By using the fractional Ito formula, we could derive the analytical solution for the real option value, which is embedded in the supply contract. The result demonstrates that the higher the degree of autocorrelation in demand, the larger the real option value. As a consequence, the wholesale price determined in the supply contract without considering demand’s long-range dependence is significantly undervalued. In conclusion, the supplier should charge more for the wholesale price when the degree of autocorrelation in demand is higher.
Proceedings of the 2013 International Conference in Management Sciences and Decision Making=2013年管理科學與經營決策國際學術研討會論文集