A Young Investment Banker Considers Issuing a DM/$ Currency Option $\bullet$

A young investment banker considers issuing a DM/$ currency option bond for a AAA client and wonders about its pricing. He knows that currency options are available on the market and that they could help set the conditions on the bond issue. As a first step, he decides to study a simple case: a one-year bond. The current market conditions are as follows:
$\bullet$ One-year dollar interest rate: 10%.
$\bullet$ One-year Deutsche mark interest rate: 7%.
$\bullet$ Spot DM/$ exchange rate: $1 =DM 2.
The banker could issue a bond in dollars at 10%, a bond in DM at 7%, or a currency option bond at an interest rate to be determined. One-year currency options are negotiated on the over-the-counter market. A one-year currency option to exchange one dollar for two Deutsche marks is quoted at 4%, that is, four cents per dollar. This is a European option, which can be exercised only at maturity. The one-year forward exchange rate is: $$F = 2 \times \frac { 1 + 7 \% } { 1 + 10 \% } .$$ a. Given these data, what should the interest rate be on a one-year DM/$ bond?
b. How would you determine how to set the interest rate on an n-year currency bond?