Problem 7.24. In an interest rate swap, a financial institution pays 10% per annum and receives three- month LIBOR in return on a notional principal of $100 million with payments being exchanged every three months. The swap has a remaining life of 14 months. The average of the bid and offer fixed rates currently being swapped for three-month LIBOR is 12% per annum for all maturities. The three-month LIBOR rate one month ago was 11.8% per annum. All rates are compounded quarterly. What is the value of the swap? Use LIBOR discounting The swap can be regarded as a long position in a floating-rate bond combined with a short position in a fixed-rate bond. The correct discount rate is 12% per annum with quarterly compounding or 11.82% per annum with continuous compounding ( 4*In(1+12%/4) =11.82%). why multiply by 0.25? how to get it? Immediately after the next payment the floating-rate bond will be worth $100 million. The next floating payment ($ million) is 0.118x100x0.23= 2.95 The value of the floating-rate bond is therefore 100.941 why multiply by 2/12? how to get it? 102.95e-0.1182X2/12 why CF is 2.5? The value of the fixed-rate bond is 2.5e-0.1182x2/12 + 2.5e-0.1182x5/12 + 2.5e0.1182x8/12 why multiply by 2/12, 5/12.... and why the interval is 3 months? +2.5e-0.1182x11/12 +102.5e -0.1182x14/12 = 98.678 The value of the swap is therefore 100.941-98.678 = $2.263million