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In this paper we provide a dynamic minimum-variance hedging strategy for firms in incomplete markets. Firms are looking for improved methods to more efficiently hedge input and output price risk exposure, but it is often the case that all price risk cannot be eliminated through exchange traded futures contracts. Since futures contracts exist for a limited number of assets some sources of price risk cannot be directly hedged and thus hedging markets are incomplete for many firms. If related futures contracts do not exist for both input and output price risk the traditional approach is to employ a one-sided hedge, that is, to hedge only for the risk source with related futures contracts and remain unhedged in the other. By identifying the price transmission (PT) mechanism between input and output prices in a classical complete-market model, we present a two-sided hedge that enables firms to minimize both input and output price fluctuations through a single tradable futures contract even in incomplete markets. Specifically, since in different industries PT is expected to vary in direction and magnitude, we consider four subcases in the model according to the direction of PT and the availability of futures contracts: (CO) cost-driving PT in which supply forces lead to equilibrium between input and output prices with output futures contracts; (CI) cost-driving PT with input futures contracts; (DO) demand-driving PT with output futures contracts; and (DI) demand-driving PT with input futures contracts. In all cases the firm can only directly hedge cash positions with futures contracts (a one-sided hedge), or jointly hedge input and output price risk with a single futures contract (a two-sided hedge) but accounting for PT. A two-factor diffusion model with a stochastic, mean-reverting convenience yield is assumed for the underlying asset. The optimal dynamic hedges are the weighted averages of the classic minimizing direct hedge and cross hedging ratios. We apply our results to the problem of a hypothetical firm that uses light sweet crude oil to produce jet fuel. The firm intends to reduce price exposure with a futures contract on light sweet crude oil. We compare hedging policies and hedging effectiveness between the one-sided and two-sided hedges. Weekly data of futures prices for light sweet crude oil for delivery to Cushing, OK, and spot prices for New York Harbor jet fuel, and spot prices for light sweet crude oil from April 4, 1990 to August, 16, 2015 are used to perform the analysis. We find that the two-sided model results in a more effective hedge. These findings suggest that jet fuel producers will most efficiently reduce profit fluctuations using a hedging model that directly accounts for vertical price links between the input and output prices. The contribution of this paper consists of devising a dynamic two-sided hedge ratio for firms to jointly hedge input and output payoffs in incomplete markets by incorporating the PT mechanism into the traditional complete-market minimizing hedging model. As PT is an important characteristic describing the overall operation of the market, this strategy may be practical for firms in multiple industries.


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