swaps question question, current, someone

tarik64

A $10 million 1-year semi-annual-pay LIBOR-based interest-rate swap was initiated 90 days ago when LIBOR was 4.8%. The fixed rate on the swap is 5%, current 90-day LIBOR is 5% and 270-day LIBOR is 5.4%. The value of the swap to the fixed-rate payer is closest to:
A) $19,229.
B) $15,633.
C) $12,465.
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im having a hard time grasping the time-lines in these and figured if i saw it from someone elses prespective might make things clearer - please show your work.

bchadwick

You are actually comparing (in this case) 2 coupns to 2 coupns.
as you know the fixed side doesn’t reset, so you need to find the value of all the future pmts discounted at the given rates.
for the floating rate you do the same thing only you are multiplying the notional by the libor rate and then discounting it by the same libor rate which gives you a value of 1.
for example:
suppose we are at a reset date and the current 180 day libor is 5%
The floater pmt would now be .05(180/360) of the notional in 180 days or .025. now, to discount that back to the present you would divide by .05(180/360) or .025.
.025 / .025 = 1
It’s easier just to add the 1 to the amount that is left untill the next reset date instead of going through this each time the floater changes.Hope that makes sense.

jcfa2011

I understand all the math behind it, but I don’t understand how the comparison is fair.
We are including 2 coupons from the fixed side, and only 1 coupon from the floating side. Why isn’t compared 1 coupon with 1 coupon?

koba

at that point you know the 2nd LIBOR rate.
so the PV(2nd Libor Rate + the Full Principal) is the floating payment…

Roflnadal

What happens after first payment day? . Let’s say you’r 10 days after first payment day? How much is the floater worth then?
I get that there is a new rate for LIBOR , set on first payment day , payable on the second payment day. Would it worth that new rate discounted by a revised LIBOR reading each day ?

svgleeson

Coupon Resets to 0…. that’s why

dvilayphet

it’s funny i was about to ask this question as well:
How do you value a floater if you are at the payment day.
So it’s just the face value. I know. my question is why don’t we add the coupon payment here. just for the understanding! sorry!
because if its 20days before expiration we always do payment plus par value.

draz

Yes it is….a bit confusing as you have to assume the payment on the floating side is out of the picture, but I guess that’s why they say it resets on those dates.

studyn

It should be 10 mil since it reset at the payment day (day 180)

kingstongal

at the payment day - coupon has reset… so it is just the face value (1$) isn’t it?