Bank PAPOUF Decides to Issue Two Bonds and Wonders What $\bullet$

Essay

Bank PAPOUF decides to issue two bonds and wonders what the fair interest rate on these bonds should be:
A. A one-year currency option bond. The bond is issued in dollars with a face value of $100. The bondholder can choose to have the coupon and principal paid in dollars or in SFr, at a specified exchange rate of SFr/$ = 2, that is, receive either $100 or SFr 200 as principal repayment, and receive either $C or SFr 2C as interest if C is the coupon set in dollars. The coupon rate is
c = C/100.
B. A two-year currency option bond. The bond is issued in dollars, with a face value of $100 and pays an annual coupon C'. The bondholder can choose to have the coupons and principal paid in dollars or in SFr, at a specified exchange rate of SFr/$ = 2, that is, receive either $100 or SFr 200 as principal repayment, and receive either $C' or SFr 2C' as interest, if C' is the coupon set in dollars. The coupon rate is c'= C'/100.
Current market conditions are given below:
$\bullet$ Interest Rates 1-Year 2-Year
Zero-coupon rates
US$ 8% 8%
SFr 4% 4%
$\bullet$ Spot exchange rate: SFr/$= 2
$\bullet$ Currency options:
SFr call, strike price 50 U.S. cents, expiration one year: 2 U.S. cents.
SFr call, strike price 50 U.S. cents, expiration two years: 5 U.S. cents.
a. Compute the coupon C on Bond A that would be consistent with market conditions at time of issue.
b. Compute the coupon C' on Bond B that would be consistent with market conditions at time of issue.