The Optimal Level of Forward Exchange Transactions

Abstract

The basic model of this paper is that of a transactor who is to receive at a specified time t in the future a fixed quantity of domestic funds Ad and a fixed quantity of foreign funds Af. It is further assumed that there exists a forward market in foreign exchange in which one unit of foreign currency can be bought and sold at a given and known forward rate rf, the domestic currency price of one unit of foreign currency. Let X be the net forward purchases of foreign exchange that the transactor undertakes at the market rate rf; a negative value of X indicates net sales of forward exchange. It is assumed that at time t the foreign currency will be convertible for the transactor at a fixed but unknown spot exchange rate and that the transactor can assess or derive a probability distribution on this spot exchange rate f(rt) for rt > 0. Finally, it is assumed that the transactor can express a utility function u on the domestic currency equivalent of his ending currency holdings. This paper considers the problem of determining the optimal level of forward exchange purchases X0.