Question 14 from schweser Fixed income ss 17 A bank entered into 1 yr currency swap w/ quarterly payment 200 days ago by agreeing to swap $1 million for 800,000 euros. The bank agreed to pay an annual fixed rate of 5% on the 800,000 euro and receive floating rate tied to LIBOR on the 1million USD. Current LIBOR/EURIBOR rates and present value factors are shown in the following table: 70d LIBOR 4.0% .9923 90d LIBOR 4.4% .9891 160d LIBOR 4.8% .9791 180d LIBOR 5.2% .9747 70d EURIBOR 5.2% .9900 90d EURIBOR 5.6% .9862 160d EURIBOR 6.1% .9736 180d EURIBOR 6.3% .9695 Current spot exchange rate = .75euro per . 90 day LIBOR is 4.2% at last payment date. What’s the value of the swap to the bank today? There is one part in the answer where Schweser claimed that coupon of $floating side=$1,000,000x(.042/4)=10,500 value of the floating side=0.9923x$1,010,500=1,002,719 while... value of the euro fixed side=.9900x10,000+.9736x810,000=798,516 euro What I don't understand is why the calculation for Value of floating side excluded the 3rd quarter coupon payment when it’s included in the calculation for Value of euro fixed side. Notice the LIBOR rate was divided by 4 to arrive at the coupon payment of $10,500 per quarter, so it doesn’t make sense to assume semi-annual payment right?
is the answer $61,969?
key part is 200 days ago… so now the only stuff left to consider are the 70d and the 160d LIBOR/EURIBOR. Original was 90, 180, 270, 360 you are 200 days forward. so 70d and 160d #s should be considered.
is the answer 61,969? =================== yes, it is. My question is since we are at day 200. Shouldn't still have two more quarterly coupons coming up on day 270 and day 360? How come the valuation for floating side only account for one?
because that is how you value the floating side. the example used is of a floating rate bond. as the coupon is reset every payment date, the par value of the bond can be higher or lower than par between coupon dates, but not on the payment of the coupon date and reset of the coupon. so on day 270, we know what the 90 day LIBOR will be and the value of the bond will be par. thus, we do not need to calculate the 360 coupon payment and the return of principal…we can just calculate 270day floating payment and the return of principal then.
1010.5*0.9923 = 1002.71915$ 10*0.99 + 810*0.9736 = 798.516E 1002.71915*0.75=752.0393625E 798.516E - 752.0393625E = 46.4766375E 46.4766375/0.75 = 61.96885$
bluecollar got it right… always remember… while valuing the floating side (whether it is currency or plan vanilla or any other swap) you consider only the upcoming coupon because on the date of the coupon the value of the floating side is reset to zero (because NPV of all other future coupon payments should match the payments from the fixed side).