Restricted Export Flexibility and Risk Management with Options and Futures

Pd + PfC = c^,(Q*). The inequality follows directly from put-call parity.¹⁰ Then, the
convexity of the cost function implies Q₁*_nflex < Q*. This proves the next corollary.

Corollary 3 When currency call options with strike price P_d/Pf are available, the (re-
stricted) export flexible firm’s optimal output is higher than that of an otherwise identical
exporting firm which possesses no export flexibility.

The opportunity to refrain from exporting at low realizations of the exchange rate
stimulates the export flexible firm to produce more. Export flexibility creates additional
value for the firm which could be sold in the currency call options market at a positive
price per unit of potential exports. This creates a wedge between the marginal cost of a
flexible firm and that of an inflexible firm as shown above.

Now, turn to the firm’s optimal risk management decision. Suppose that the currency
futures and options markets are jointly unbiased: F = E[S] and C = E[max(S-Pd/Pf, 0)].
Joint unbiasedness implies that the firm’s expected profits are unaffected by its positions
in the currency futures and options markets. Using the covariance operator, Cov[∙], con-
ditions (6) and (7) can be written as

Cov ^[U ^,(Π *),S?] =0,                                 (9)

Cov[u^,(Π*), max(S - Pd/Pf, 0)^] = 0.                      (10)

Rewrite the firm’s profits as

Π = S[Pf Qf - H] + maχ(S - Pd/Pf, 0)[Pf(Q - Qd - Qf ) - Z] + J (11)

where J = CZ+ FH+ Pd(Q - Qf) - c(Q). Substituting H = PfQf and Z = Pf(Q - Qd -
Qf) into equation (11) yields Π = J, which is non-stochastic. Inspection of conditions
(9) and (10) reveals that these two equations hold simultaneously at these values of H
and Z since U^,(∙) is constant if Π is deterministic, which in turn implies zero covariances.

¹⁰By put-call parity, the premium of a put option with strike price P_d/Pf must equal C plus P_d/Pf
minus F, where the option premiums are compounded to date 1. Since the put option premium is
positive, C + Pd/Pf > F .

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