A Cournot-Stackelberg Model of Supply Contracts with Financial Hedging (Based on joint work with Rene Caldentey)

             Department of Systems Engineering and Engineering Management
                     The Chinese University of Hong Kong
Date: Friday, November 27, 2020, 4:30pm to 5:30pm (Hong Kong time)
Title: A Cournot-Stackelberg Model of Supply Contracts with Financial Hedging (Based on joint work with Rene Caldentey)  
Speaker: Prof. Martin Haugh
We study the performance of a stylized supply chain where N identical retailers and a single producer compete in a Cournot-Stackelberg game. The retailers purchase a single product from the producer and afterwards sell it in the retail market at a stochastic clearance price. We assume the retailers’ profits depends in part on the realized path or terminal value of some tradeable financial market such as a foreign exchange rate, commodity index or more generally, any relevant economic index. We therefore consider a variation of the traditional wholesale price contract that is offered by the producer to the retailers. Under this contract, at t = 0 the producer offers a menu of wholesale prices to the retailers, one for each realization of the financial process up to some future time τ. The retailers then commit to purchasing at time τ a variable number of units, with the specific quantity depending on the realization of the process up to time τ. We assume the retailers are budget constrained, however, and are therefore limited in the number of units they may purchase from the producer. The supply chain might therefore be more profitable if the retailers were able to shift some of their budgets from states where the budget constraint is not binding to states where it is. In order to affect such a reallocation, we assume the retailers are also able to trade dynamically in the financial market in [0,τ]. In addition to hedging their budget constraints, we also assume the retailers can borrow in the financial market at time τ in order to increase the amount of inventory they can procure at that time. This borrowing is costly but nonetheless can complement the hedging activities of the retailers. We completely characterize the resulting Cournot-Stackelberg equilibrium and compare it to various benchmarks including a centralized supply chain as well as equilibria where one or both of hedging / borrowing are not available to the retailers. We show there is a pecking order to the hedging and debt components of the financial markets. Specifically, hedging is used at low and intermediate budget levels while debt is only used at low budget levels. When viewed as a function of the budget B, we observe a discontinuity in the full Cournot-Stackelberg equilibrium at an endogenous threshold B where the retailers begin to borrow from the debt markets. This result is surprising because for a fixed price menu, these quantities are continuous in the Cournot equilibrium. We also study the impact of retail competition on the equilibrium. We show that higher levels of competition in the retailers’ market increase supply chain efficiency, consumers’ surplus and social welfare when the retailers’ budgets are either high or low. For intermediate budget levels, however, it’s possible that too much retailer competition can have a detrimental effect on these measures. Finally, we relate this work to the problem of production postponement and show how our formulation can be adapted to include a timing component to the ordering problem.
Martin Haugh is an Associate Professor of Analytics and Operations Research at Imperial College, London. He joined Imperial's Business School in 2017 after spending more than 10 years in the Department of IE & OR at Columbia University as well as 4 years working in the hedge fund industry in New York and London. He obtained his PhD in Operations Research from MIT in 2001 and has MS degrees in Mathematics and Applied Statistics from Cork and Oxford, respectively. His research interests are in computational finance and risk management, dynamic programming, and data analytics.
Friday, November 27, 2020 - 16:30 to 17:30