Commodity options purchasing and credit financing under capital constraint

This paper investigates a purchasing contract with options under capital constraint and credit support from a financial institution. The buyer, who has limited capital, can buy commodity options and a fixed order, and choose to exercise all or part of the options at a later time. We characterize the buyer׳s optimal ordering strategy with limited capital. There is one critical value for the capital; that is, the buyer will only purchase a fixed order when the capital is less than the value. With more capital, the buyer will reduce the fixed order quantity and increase the option orders until the capital is used up or the global optimization is reached. This result implies that the option is a risk-hedging tool only for easy finance companies. Furthermore, we find that when the buyer obtains funding from a financial institution such as a bank, the buyer׳s profit will be increased with bank financing, and the buyer׳s optimal purchasing decision will follow the similar policy and order less options and more fixed orders compared with the case when there is sufficient capital. Numerical examples are provided to demonstrate the theoretical results.