Optimal hedging with currency forwards, calls, and calls on forwards for the competitive exporting firm facing exchange rate uncertainty

Abstract

We extend the well-known full hedge theorems of the hedging literature to random profits that are nonlinear in the random exchange rate. This arises when production flexibility is added to the standard model of the risk-averse exporting firm, where all production decisions have to be made before the exchange rate is known. Hence, hedging with currency derivatives that provide a linear payoff in the exchange rate can no longer provide a perfect hedge. Therefore forward selling is replaced by writing a certain call portfolio. Adding delayed revenue to the model induces the firm to sell calls on forwards. Because our generalized full hedge proposition is proved for random profits that might as well decrease in the exchange rate, the result is applicable to certain types of importing firms, too. — Given the absence of speculative motives on the part of the firm, it turns out that long-term investments in capital goods are chosen in risk-neutral manner.