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)* (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* (1+0.05)/(1+0.03) \\ \\ =1.50* (1.05)/(1.03) =1.50*1.019 \\ \\ =\bold{\$1.5291}`