Question

Under the terms of an interest rate swap, a financial institution has agreed to pay 10% per annum and to receive six-month LIBOR in return on a notional principal of $100 million with payments being exchanged every 6 months. The swap has a remaining life of 4 months. The average of the bid and offer fixed rates currently being swapped for 6-month LIBOR is 12% per annum for all maturities. The 6-month LIBOR rate two months ago was 11% per annum. All rates are compounded semiannually. What is the value of the swap?

Answer 1

The underlying function of the swap is to exchange two different cash flows i.e. a person paying a fixed rate can opt to exchange his cashflow with a person paying a floating interest rate.

The Swap in this case will be valued on the net benefit of the swap. The benefit in this case will be availed after 4 months so it will have to be discounted to today.

1 -First we calculate the payment on the fixed end of the swap i.e. fixed interest cashflows:- so for 6 months the cashflow is 5% * $100 million = $5 million (remeber the 10% is annual). Now we discount this by the 6-month rate in effect i.e. 12% per annum (compounded5) so effectively will be 5.83% ((1.12)^0.5 -1)) for 6 months

PV (present value fixed rate) = 5 /[1+(5.83%*4/6) = $4.813 million

2 - Floating end of the swap - floating rate 6 months ago was 11% hence the coupon to be recieved at end of 6 months is $10 million x 5.3565% (remember the annual rate - 11% is compounded semi annualy so 6 monthly rate will be root of 11%).

Amount recievable at end of 6 months $10 million x 5.3565% = $5,356,500

Next we discount this value till today (4 months prior to payout) = 5,356,500 / [1+(5.83%*4/6) = $5,165,100

Hence the value of the swap is difference between floating rate vs fixed rate payout = $5,165,100 - $4,812,937 =$352,163