Restricted Export Flexibility and Risk Management with Options and Futures

Due to the uniqueness of the optimum, the firm’s optimal hedge portfolio is indeed given
by H * = Pf Qf and Z * = Pf (Q* — Qd — Qf ). This hedge portfolio makes the firm’s
profits riskless but does not change its expected value, given the joint unbiasedness of the
currency futures and options markets. Hence, this portfolio is optimal. This establishes
the following proposition.

Proposition 2 (Full hedging) Suppose that the currency futures and options markets
are jointly unbiased. The restricted export flexible firm’s optimal hedge position, (H^*, Z^*),
satisfies H^* = PfQf and Z^* = Pf (Q^* — Qd — Qf).

The optimal futures position is aimed at hedging the exchange rate exposure created by
selling the minimum level Qf in the export market against foreign currency. As is obvious,
the minimum sales requirement for the export market directly affects the optimal futures
position.

The optimal call option position, on the other hand, is used to hedge the conditional
exchange rate exposure created by export flexibility. The existence of additional foreign
exchange revenue of Pf (Q^* — Qd — Qf) is conditional on the exchange rate exceeding
Pd/Pf . By writing call options on this amount with strike price Pd/Pf , the firm creates
a conditional obligation to deliver foreign exchange. Since the firm becomes less export
flexible the higher the minimum levels of domestic sales and exports, Qd and Qf , the
optimal call option position declines in these parameters.

The firm’s net foreign currency position sums up to zero. For exchange rate realizations
below P_d/Pf , the call options are not exercised and the optimal futures position provides a
full hedge for the export revenue of PfQf . For exchange rate realizations ab ove Pd/Pf , the
call options are exercised. In both cases, the firm has to deliver its entire foreign exchange
revenue in order to satisfy the obligations from the hedge portfolio (H^* , Z^*). Therefore,
the optimal portfolio of futures and call option positions makes the firm’s profits invariant
to different realizations of the exchange rate (full hedging). These hedging mechanics are
illustrated in Figure 3.

13

<<   11   12   13   14   15   16   17   >>

More intriguing information