Derivatives Question help!

Question

I have the following question: Consider a $5 million semiannual-pay floating equity swap initiated when the equity index is 760 and 180-day LIBOR is 3.7%. After 90 days the index is at 767, 90-day LIBOR is 3.4 and 270-day LIBOR is 3.7. What is the value of the swap to the floating rate payer?I have worked out the value of the fixed rate payer and trying to work out the value of the floating rate payer, but I can't figure out what the coupon should be at day 90 for the floating rate. Please help! I'm not sure what information to use for this part.

Stuj79 · Answer

Well it's a semi-annual pay so that is a payment every 180 days...which is set by taking half the annual LIBOR rate at the start of the period.So after 90 days have passed, we are 90 days away from the first payment, the floating side of which was set by half the 180 day LIBOR rate, 90 days ago...The initial LIBOR rate of 3.7% / 2 = 1.85% - so sat at day 90, the first payment, due in 90 days is 1.85%.So basically, the first floating payment is set by the LIBOR in existence at initiation of the swap.

googs1484 · Answer

equity index payer has exposure of 767/760-1= 92BPS in those 90 days. Floating rate payer receives .92%.At initiation of the floating rate side it would be 3.7/2= 1.85%. At t=0 the bond is equal to par. On day 180 floating rate payer pays .0185 per $1 of notional. In this case $92,500 payment at day 180. Now, 90 days in we need to find the PRESENT VALUE of that $92,500 using the NEW 90 day LIBOR rate. $92,500/(1+(3.4*(90/360))=$91,720.38Value of swap to floating rate payer is .0092 x 5 million= $46,000 (present value received from equity portion). Then he/she pays the present value of the semi annual payment of $92,500 (.0185 x 5 million) discounted at the 90 new libor rate which, as stated previously, is $91,720.38.The floating right side has a value of $46,000-$91,720.38= -$45,720.38. Zero sum game so the equity payer has the opposite sign.