Foreign exchange

Forward foreign exchange is foreign currency deliverable in the future. Its price is
called forward exchange rate or the forward outright rate, and the differential of
the forward minus the spot exchange rate is called the swap rate (not to be confused
with the rate on plain-vanilla interest rate swaps).
To apply the general mechanics of a forward transaction described above to this
case, let rt,T and r*t ,T represent the domestic and foreign money-market interest rates.
The spot and forward outright exchange rates are St and Ft,T, expressed in domestic
currency units per foreign currency unit.
To create a synthetic long forward,
Ω Borrow St/(1òr*t,Tq) domestic currency units at rate rt,T and buy 1/(1òr*t,Tq)
foreign currency units. Deposit the foreign currency proceeds at rate r*t ,T. There is
no net cash outlay now.
Ω At time T, the foreign currency deposit has grown to one foreign currency unit,
and you must repay the borrowed
St(1òrt,T q)
1òr*t ,T q
including interest. This implies that the forward rate is
Ft,Tó1òrt,T q
1òr*t ,T q
St
Here is a numerical example of this relationship. Suppose the Euro-dollar spot exchange rate today is USD1.02 per Euro. Note that we are treating the US dollar as
the domestic and the Euro as the foreign currency. Suppose further that the US
1-year deposit rate is 5.75% and that the 1-year Euro deposit rate is 3.0%. The
1-year forward outright rate must then be
1.0575
1.03
1.02ó1.0472
Typically, forward foreign exchange rates are quoted not as outright rates but in
terms of forward points. The points are a positive or negative quantity which is
added to the spot rate to arrive at the forward outright rate, usually after dividing by
a standard factor such as 10 000. In our example, the 1-year points amount to
10 000 · (1.0472ñ1.02)ó272. If Euro deposit rates were above rather than below US
rates, the points would be negative.