Question

A $100 million interest rate SWAP has a remaining life of 12 months. Under the terms of the SWAP the 6-month LIBOR rate is exchanged for 4%/year compounded semi-annually (you pay the LIBOR rate and receive the fixed rate). The current six-month LIBOR rate is 4.5%/year with semi-annual compounding and the forward LIBOR rate between 6 months and 12 months is 4.75%/year with semi-annual compounding. What is the current value of the SWAP? Use a risk-free rate of 3%/year to discount both cash flows. Please explain your answer.

Answer 1

From the point of view of Fixed rate payer

Net amount received after 6 months = $100 million *4.5%/2 - $100 million * 4%/2

= $250,000

Net amount received after 12 months = $100 million *4.75%/2 - $100 million * 4%/2

= $375,000

Assuming the discount rate also to be compounded semiannually

Value of swap to fixed rate payer = 250000/(1+0.03/2) +375000/(1+0.03/2)^2 = $610303.57

So, the current value of swap  for the fixed rate payer is $610303.57

So the value of Swap for us (floating rate payer) is -$610303.57

The value to the floating rate payer is negative as the floating rate payer is expected to pay on a net basis during the remaining 12 months.