Restricted Export Flexibility and Risk Management with Options and Futures



exchange rate changes.

It will be shown that the separation theorem can be derived even in the absence
of currency futures. If currency futures and options are fairly priced, it is optimal to
fully hedge with a portfolio that consists of both currency futures and options. The
joint use of these derivatives is due to the fact that the restricted export flexible firm’s
exposure is piecewise linear in the exchange rate with strictly positive slope everywhere.
In addition, the paper analyzes optimal production and risk management decisions when
there are no currency options available. It is also shown that making fairly-priced currency
options available to the firm enhances production provided the currency futures market
is unbiased.

The argument for the joint use of currency futures and options proposed in this paper
has the advantage of being particularly simple since it relies on a one-period model with
one single source of risk. Other models explaining the joint use of futures and options are
much more complex since they either require the existence of several sources of risk as in
Lapan et al. (1991), Lapan and Moschini (1994), Moschini and Lapan (1995), Broll et al.
(2001), Frechette (2001) and Mahul (2002) or a multi-period framework as in Lence et al.
(1994).

The model which comes closest to the spirit of ours is the model of Moschini and
Lapan (1992) who analyze a competitive firm with production flexibility under output
price uncertainty. In their model, there are two types of inputs. The decision on the use of
quasi-fixed inputs has to be made before price uncertainty is resolved whereas the decision
on other inputs can be made under certainty. Hence, this firm’s flexibility is restricted
by the obligation to decide on the level of quasi-fixed inputs before price uncertainty is
resolved. Moschini and Lapan (1992) show that the optimal hedging portfolio consists
of both futures and options if the profit function is quadratic and the price distribution
is symmetric. In contrast to their model of restricted production flexibility, we analyze
restricted export flexibility without imposing a similar symmetry requirement on the
distribution. However, the profit function analyzed by Moschini and Lapan (1992) is



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