Restricted Export Flexibility and Risk Management with Options and Futures

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The firm makes its
production and risk
management decisions.

The firm observes the
exchange rate.

The firm makes its
export decision and
realizes profits.

Figure 1: Time line

However, it seems realistic that export flexibility is restricted to some extent. Due to
various explicit and implicit obligations, the firm has to maintain certain minimum levels
of domestic sales and exports. These quantities are exogenously given and are denoted by
Q_d for the domestic market and by Qf for the foreign market. Thus, the firm’s flexibility
only applies to the amount of output which exceeds the sum of these minimum levels of
domestic sales and exports, i.e. restricted flexibility only applies to Q - Qd - Qf > 0.

Given an exchange rate realization S and the firm’s restricted export flexibility, its
optimal decision on the allocation of output between the domestic and foreign markets is
as follows: If SPf > Pd , the domestic currency revenue from exporting is higher than that
from selling in the domestic market. Hence, the firm exercises its real option and exports
as much as possible to the foreign market, Q-Qd, while still meeting the minimum level of
domestic sales, Qd . For SPf ≤ Pd , the firm maintains only the minimum level of exports,
Qf , and sells the rest, Q - Qf , in the domestic market. It is assumed that there is at
least some probability mass for realizations of S below Pd/Pf and at least some mass for
realizations above this value, S < Pd/Pf < S.

Given the optimal sales allocation rule, the firm’s domestic currency revenue, RR, is
given by

( SPf Qf + Pd(Q - Qf ) if SPf ≤ Pd,

R =                                                               (1)

( SPf (Q - Qd) + PdQd if SPf > Pd.

Writing the above equation in a compact way yields
~ ~ . . . ~ . . . . . _ . .
R = SPfQf + Pd(Q - Qf) + Pf maχ(S - Pd/Pf, 0)(Q - Qd - Qf).       (2)

It is evident from the last summand in equation (2) that there are options embedded in the

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