Question

Suppose you observe a spot exchange rate of $1.50/€. if interest rates are 5% apr in the u.s. and 3% apr in the euro zone, what is the no-arbitrage 1-year forward rate? $1.5291/€ €1.4714/$ €1.5291/$ $1.4714/€

Answer 1

The no-arbitrage 1-year forward rate in $/€, F($/€) is given by

$F(\ /euro)=S(\ /euro)\times \frac{1+i_\ }{1+i_{euro}}$

where S($/euro) is the spot exchange rate in $/€, $i_$ is the interest rate in the US and $i_{euro}$ is the exchange rate in the Euro zone.

Thus, given that the spot exchange rate is $1.50/€ and interest rates are 5% apr in the u.s. and 3% apr in the euro zone.

The no-arbitrage 1-year forward rate is given by:

$F(\ /euro)=1.50\times \frac{1+0.05}{1+0.03} \\ \\ =1.50\times \frac{1.05}{1.03} =1.50\times1.019 \\ \\ =\bold{\ 1.5291}$