Volume 16 | Issue 4 | Article 1
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Basis Risk and Optimal Hedging of a Purchase Decision
We model a purchaser’s choice of the optimal order quantity for a commodity and optimal index option hedge that minimizes the expected disutility of hedged cost (1) when the order must be placed before demand is revealed, (2) the commodity price and demand are uncertain, and (3) the index differs from the commodity price, thus contributing basis risk. We assume that the index, commodity price, and demand follow a joint trivariate lognormal distribution and develop the necessary formulae for the expected value of the option, variance of the option value, covariance between the option value and the commodity price, and between the option value and the cost of an unhedged purchase strategy. Our numerical analysis shows that the optimal index option hedge performs better if the correlation between the index and the demand for the commodity is high, and, surprisingly, if the correlation between the index and the commodity price is low.
