Restricted Export Flexibility and Risk Management with Options and Futures

compromise between these two futures positions. The dependence of the firm’s profits on
the exchange rate, given the optimal futures position, is depicted by the V-shaped line in
Figure 4.

Proposition 4 shows that the interval containing H* narrows if either Qd or Qf in-
creases. Tightening the restrictions on the firm’s export flexibility means that the con-
vexity of unhedged profits in Figure 4 becomes smaller. This reduces the conflict between
hedging for high and hedging for low exchange rate realizations. In the limit, for a firm
without any export flexibility, the interval degenerates and the convexity of unhedged
profits disappears. Then, the optimal futures position is unequivocally determined and
the present model reduces to the classical model of an inflexible exporting firm as analyzed
by Benninga et al. (1985) and others.

Finally, it is of interest to compare Q* and Q* in order to find out whether introducing
fairly-priced currency options to the firm stimulates production, thereby expected exports
and expected domestic sales. Using the above notation for an unbiased currency option,

C = E[max(S - Pd/Pf, 0)], condition (14) can be written as

Comparing condition (16) with the optimality condition in Proposition 1, c^z(Q*) =

Pd + PfC, yields c^z(Q*) > C(QX) if and only if the covariance term in equation (16)
is negative. It then follows from the convexity of the cost function that Q* > Q*. Signing
the covariance in equation (16) requires some tedious algebra. As the following proposi-
tion indicates, this covariance term is indeed negative if the currency futures and options
markets are jointly unbiased. A proof is relegated to Appendix B.

Proposition 5 Suppose that the currency futures and options markets are jointly unbi-
ased. Then, making currency options with strike price P_d/Pf available to the firm en-
hances production.

The intuition behind this result is as follows. Introducing fairly-priced currency options
allows the firm to sell the risk associated with the option to export without altering its

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