Question

In an interest rate swap offered by a bank, Company A could pay 3.5% per annum and receive six-month LIBOR in return on a notional principal of $100 million with payments being exchanged every six months. The swap has a remaining life of 16 months. Six-month forward LIBOR for all maturities is currently 3.8% per annum. The six-month LIBOR rate two month ago was 3.2% per annum. OIS rates for all maturities are currently 3.0% with continuous compounding. All other rates are compounded semiannually.

What is the value of the swap?

Answer 1

The value of swap to A = value of the floating rate bond received by A - value of Fixed rate bond paid by A

We know that value of a floating rate bond immediately after a coupon is paid is equal to the face value( notional principal) . So, the floating rate bond pays 3.2%/2 on $100 milion i.e. $1.6 million plus $100 million after 4 months  

Value of the floating rate bond = 101.6* exp(-0.03*4/12) = $100.589 million = $100,589,063.11

The fixed rate bond pays 3.5%/2*$100 million = $1.75 million after 4 months, 10 months and 16 months along with principal redemption of $100 million after 16 months

So, value of fixed rate bond

= 1.75*exp(-0.03*4/12)+1.75*exp(-0.03*10/12)+1.75*exp(-0.03*16/12)+100*exp(-0.03*16/12)

=$101.199705 million

= $101,199,704.99

So, value of swap to A = $100,589,063.11- $101,199,704.99 = -$610641.88