Suppose that the yield curve is flat at 5% per annum with continuous compounding. A five-year swap with a notional principal of $100 million in which 6% per annum with semi-annual compounding is received and six-month LIBOR is paid will last another 15 months. Payments are exchanged every six months. The six-month LIBOR rate at the last reset date (three months ago) was 7% per annum with semi-annual compounding. Answer in millions of dollars to two decimal places (3.1) What is the value of the fixed-rate bond embedded in the swap? (3.2) What is the value of the floating-rate bond embedded in the swap? (3.3) What is the value of the swap for the floating rate payers?
(3.4) The first ever coupon of the swap paid to the floating rate receiver was $5.5 million. What was the continuously compounded floating interest rate with a 6-month maturity when the swap was initiated? Hint: how is the floating rate coupon determined?