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Optimal Foreign Exchange Risk Hedging: Closed Form Solutions Maximizing Leontief Utility Function

DOI: 10.4236/tel.2018.814181, PP. 2893-2913

Keywords: Foreign Exchange, Risk, Optimal Hedging, Closed Form Solution

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Abstract:

In this paper, we extend Kim (2013)for the optimal foreign exchange (FX) risk hedging solution to the multiple FX rates and suggest its application method. First, the generalized optimal hedging method of selling/buying of multiple foreign currencies is introduced. Second, the cost of handling forward contracts is included. Third, as a criterion of hedging performance evaluation, there is consideration of the Leontief utility function, which represents the risk averseness of a hedger. Fourth, specific steps are introduced about what is needed to proceed with hedging. There is a computation of the weighting ratios of the optimal combinations of three conventional hedging vehicles, i.e., call/put currency options, forward contracts, and leaving the position open. The closed form solution of mathematical optimization may achieve a lower level of foreign exchange risk for a specified level of expected return. Furthermore, there is also a suggestion provided about a procedure that may be conducted in the business fields by means of Excel.

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