Problem 1: Suppose that 6-month, 12-month and 18-month zero rates are 4%, 4.5% and 4.8% per annum with continuous compounding respectively. What is the cash price of a bond with a face value of 1,000 that will mature in 18 months and pays a coupon rate of 5% per annum semiannually?

102.04

98.04

100.22

112.02

Problem 2:

In early 2012, the spot exchange rate between the AUD and USD was 0.98 ($ per AUD). Interest rates in the U.S. and Switzerland were 7% and 5% per annum,respectively, with continuous compounding. What arbitrage strategy is possible when 2-year forward exchange rate is 1.04?

No arbitrage since theoretical forward price is equal to the current 2-year forward exchange rate.

a. borrow 1,000 AUD at 7% for 2 years and convert to USD at spot 0.98 now and invest at 5%. At the same time enter into a forward contract to buy AUD 2years later at 1.03 forward exchange rate.

b. borrow 1,000 AUD at 5% for 2 years and convert to USD at spot 0.98 now and invest at 7%. At the same time enter into a forward contract to buy AUD 2years later at 1.03 forward exchange rate.

c. borrow 1,000 USD at 5% for 2 years and convert to USD at spot 0.98 now and invest at 7%. At the same time enter into a forward contract to sell AUD 2years later at 1.03 forward exchange rate.

d. borrow 1,000 USD at 7% for 2 years and convert to AUD at spot 0.98 now and invest at 5%. At the same time enter into a forward contract to sell AUD 2years later at 1.03 forward exchange rate.