Restricted Export Flexibility and Risk Management with Options and Futures



Proposition 1 (Separation) When currency call options8 with strike price Pd/Pf are
available, the restricted export flexible firm’s optimal output, Q*, is implicitly given by
c'(Q*) = Pd + PfC. Thus, Q* depends neither on the preferences of the firm nor on the
distribution of the exchange rate.

Since the derivation of cz(Q*) = Pd + Pf C does not involve equation (6), i.e. the use
of currency futures, the above separation result holds even when H
0. The intuition
behind Proposition 1 can be explained using the thin dashed line in Figure 2 which exhibits
the firm’s marginal revenue with respect to the exchange rate as given by P
d + Pf max(S
Pd/Pf, 0). Since the shape of this function exactly mirrors the shape of the call option’s
payoff (plus a constant), call options with strike price P
d/Pf span the firm’s exchange rate
exposure. Thus, the production decision is based on the market price for this exposure
as given by the call premium C . The optimal production decision is to equate marginal
costs with deterministic marginal revenue. If the condition of Proposition 1 is violated,
the firm can make a riskless profit. If, for example, output is less than
Q*, then increasing
output and selling the associated exchange rate exposure by writing a call option on P
f
units of foreign currency results in a deterministic profit of Pd + PfC cz(Q) > 0. Hence,
the degree of risk aversion and the distribution of the exchange rate cannot affect the
optimal production decision.

A natural question to ask in the context of restricted export flexibility is whether the
tightness of the restrictions affects the firm’s optimal output. The following statement is
a direct consequence of Proposition 1.

Corollary 1 When currency call options with strike price Pd/Pf are available, the re-
stricted export flexible firm’s optimal output,
Q*, is not affected by the tightness of the
restrictions arising from
Qd and Qf .

This result is a direct implication of the optimality condition, cz(Q*) = Pd + PfC,
which is unaffected by Q
d and Qf . Since marginal revenue is independent of Qd and Qf ,

8 Due to put-call parity, the availability of currency futures and put options yields the same result.

10



More intriguing information

1. The name is absent
2. The name is absent
3. The name is absent
4. On the job rotation problem
5. The name is absent
6. The Triangular Relationship between the Commission, NRAs and National Courts Revisited
7. Initial Public Offerings and Venture Capital in Germany
8. Wirtschaftslage und Reformprozesse in Estland, Lettland, und Litauen: Bericht 2001
9. Modelling the health related benefits of environmental policies - a CGE analysis for the eu countries with gem-e3
10. Opciones de política económica en el Perú 2011-2015