e price at time
a contract to exchange
for
at a future time
and for fixed exchange rate
.
We determine a fair forward exchange rate
by the following argument. We purchase
units of riskless
-bond,
short one riskless
-bond
with maturity at
and enter into the exchange contract in question. The forward exchange rate
that makes such position of zero value is the correct exchange rate. These are
the
-values
of the replicating
position:
where we used
by definition of the bond and offset the contract in question at time
.
We obtained two equations for two unknown variables
and
.
The solution
is
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(Forward exchange rate)
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