In an interest rate swap, a financial institution has agreed to pay 3.6% per ann
ID: 2780443 • Letter: I
Question
In an interest rate swap, a financial institution has agreed to pay 3.6% per annum and to receive 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. Three-month forward LIBOR for all maturities is currently 4% per annum. The three-month LIBOR rate one month ago was 3.2% per annum. OIS rates for all maturities are currently 3.8% with continuous compounding. All other rates are compounded quarterly. What is the value of the swap?
Explanation / Answer
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 3.8% per annum with quarterly compounding or 3.2% per annum with continuous compounding.
Immediately after the next payment the floating-rate bond will be worth $100 million. The next floating payment ($ million) is
3.2% X 100 /4 = 0.8
The value of the floating-rate bond is therefore
100.8e^(-0.032*2/12) = 100.263
The value of the fixed-rate bond is
0.9e^(-0.032*2/12)+0.9e^(-0.032*5/12)+0.9e^(0.032*8/12)
+0.9e^(0.032*11/12) + 100.8e^(0.032*4/12) = 105.510
The value of the swap is therefore
100.263- 105.510 = -5.247 Million
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.