# In an interest rate swap offer

In an interest rate swap offered by a bank, Company A could pay3.5% per annum and receive six-month LIBOR in return on a notionalprincipal of \$100 million with payments being exchanged every sixmonths. The swap has a remaining life of 16 months. Six-monthforward LIBOR for all maturities is currently 3.8% per annum. Thesix-month LIBOR rate two months ago was 3.2% per annum. OIS ratesfor all maturities are currently 3.0% with continuous compounding.All other rates are compounded semiannually.

(a) What is the value of the swap?

(b) Besides being able to choose a swap that pays a fixed rateof 3.5%, Company A could choose a swap that pays a floating rate ofsix-month Libor – 0.1% for business with the bank. The correspondchoices for Company B are 4.6% and six-month Libor + 0.5%,respectively. Explain how could Company A gets a more favorableinterest rate swap than the one the bank offers.

swap to A = the floating rate bond received by A – Fixed ratebond paid by A

the value of a floating rate bond immediately after a coupon ispaid is equal to the face value( notional principal) .

therefore, the floating rate bond pays 3.2%/2 on \$100 milioni.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 millionafter 4 months, 10 months and 16 months along with principalredemption 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

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