B1. Fixed-for-floating interest rate swaps XYZ, Corp. has just entered into a forward-starting interest rate swap under which it will pay 3-month LIBOR and receive fixed payments corresponding to an annualized fixed rate of 2.5% (with quarterly compounding). Under the swap, the payments are exchanged at two dates only, in 9 months and in 12 months. The notional for this swap is 150m GBP.

The 3-month LIBOR rate is 2% with quarterly compounding, and the 6-month LIBOR rate is 2.1% with semiannual compounding. Bond A has a remaining maturity of 9 months pays a coupon of 4% per annum semiannually, and is currently trading at a price of 102% of face value. Bond B has a remaining maturity of 12 months pays a coupon of 3% per annum semiannually, and is currently trading at a price of 100% of face value.

a. From the information given, compute

i. the 9-month and the 12-month spot rates with quarterly compounding, and

ii. the forward rate that starts applying in 6 months and pays off in 9 months, and the forward rate that starts applying in 9 months and pays off in 12 months, both with quarterly compounding. [11 marks]

b. Work out the value of the fixed-rate bond and the floating rate bond underlying the swap. Hence, work out the value of the swap to XYZ. [12 marks]

c. Verify that you obtain the same result when working out the value of the swap by assuming that forward rates will be realized. [12 marks]