An interest rate swap with a principal of $100 million involves the exchange of 1.20% per annum (semi-annually compounded) for 6-month LIBOR. The remaining life is 14 months. Interest is exchanged every 6 months and the 2 month, 8 month and 14 month continuously compounded zero rates are 0.75%, 0.85% and 0.95%. The 6- month LIBOR was 1% four months ago. What is the value of the swap today?

The Value of Swap can be found in terms of floating and fixed rate Bonds

where

The Fixed rate bond pays $100 million *1.2%* 1/2 = $0.6 million after 2 months, 8 months and 14 months as well as $100 million maturity value after 14 months

So,

value of Fixed rate bond (million $)

= 0.6*exp(-0.0075*2/12)+0.6*exp(-0.0085*8/12)+100.6*exp(-0.0095*14/12)

=$100.687033 million

The Floating rate bond's value after 2 months (after payment) will be the same as Principal amount

So, the floating rate bond pays $100 million *1%*1/2 = $0.5 million +$100 million =$100.5 million after 2 months

So, value of Floating rate bond = $100.5 million *exp(-0.0075*2/12) = $100.374453 million

Thus, value of swap today for the floating rate payer

= $100.687033 million - $100.374453 million

=$ 0.31257937 million

or $312,579.37