more general than ours. In both models, the joint use of futures and options is optimal.
The paper is organized as follows. Section 2 delineates the model. Section 3 charac-
terizes the firm’s optimal production and risk management decisions when both currency
futures and options are available. Section 4 derives the firm’s optimal production and risk
management decisions when there are currency futures only. Section 5 concludes.
2 The model
Consider a risk-averse competitive firm which produces a single commodity Q. The cost
function is c(Q), where c(0) ≥ 0, c,(Q) > 0 and c"(Q) > 0. The firm supplies its entire
output to two markets: the domestic and a foreign market. The per-unit price in the
domestic market, Pd , is denominated in domestic currency. The per-unit price in the
foreign market, Pf , is denominated in foreign currency. Pd and Pf are fixed and known
to the firm. Due to the segmentation of the domestic and the foreign market, commodity
arbitrage is unprofitable so that the law of one price does not necessarily hold.
At date 0, when the firm makes its production decision, it does not know the exchange
rate (in units of domestic currency per unit of foreign currency). The exchange rate,
denoted by S4, is distributed according to a cumulative distribution function, G (S), over
support [S, S], where 0 ≤ S < S < ∞. Prior to making its export decision at date 1, i.e.
before the sales allocation between the domestic and foreign market, the firm observes
the realization of the exchange rate. For high exchange rate realizations, it is attractive
to export since the domestic currency value of the firm’s foreign exchange revenue is also
high. In contrast, for low exchange rate realizations, the firm will sell on the domestic
market. Hence, the sales allocation decision at date 1 depends on the realization of the
exchange rate. In this sense, the firm is export flexible. The possibility to export can thus
be regarded as a real option held by the firm. This option is exercised if the exchange
rate is sufficiently high. The time structure is summarized in Figure 1.
4Throughout the paper, random variables have a tilde (~) while their realizations do not.