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.
（thank you for your help)
Answer:
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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