Forward Exchange Rates

Given the frequent long times required for completing international transactions an active market for currency exchanges that are agreed at some present time, but not completed until some later time exists. A major group of these transactions are known as forward contracts. At the initiation of a forward contract two participants known as counterparties to the transaction agree to several things. An amount of one currency that will be exchanged for an amount of another currency are agreed. Second, the scheduled time for that exchange is agreed. Dividing the amount of the first currency by the amount of the second currency involved in the transaction determines the agreed forward exchange rate for the transaction.
Banks commonly determine appropriate forward exchange rates and stand ready to offer these contracts to customers. The technique used by banks to determine forward exchange rates is relatively straight forward.

Calculating forward rates

Four inputs are needed to estimate a forward rate. These are the current spot exchange rate, S, the interest rates in each of the two currencies, the domestic and the foreign, rd and rf, and the time until the exchange is to be completed, t. From these you can calculate the forward rate, F as follows.

(1)
\begin{align} S \times\frac{1+r_d}{1+r_f}=F \end{align}

Note that if we express the spot and forward rates in terms of their components, say dollars per pound, we would have

(2)
\begin{align} S\frac{dollars}{pounds} \times\dfrac{1+r_d}{1+r_f}=F\frac{dollars}{pounds} \end{align}

The important point to observe here is that the numerator for all three terms is in the same units and the denominator for all three terms is in its same units. The obvious implication you can draw from this is that the equation works equally well for both direct and indirect quotes. You simply need to sustain the consistency of units as shown here.
$\copyright$ Arlyn R. Rubash 2011

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