swaps question question, current, someone

PieMan

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.


____________________________________________

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.

tarunajwani

at that point you know the 2nd LIBOR rate.

so the PV(2nd Libor Rate + the Full Principal) is the floating payment...

CP

luda002

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?

huangxiaoxie

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.

bdavi77962

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 ?

SpyAli

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

CP

ninja1024

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.

zephyranalyst

I'm sorry... I'm still having trouble with this.

I understand that the floating rate note resets to par at the reset dates. I also understand that you will not know the cash flow for the second floating payment until the coupon rate is set (in 90 days in this case).

What I don't understand is why we don't care about this other future cash flow. In 90 days, the floating rate note will pay the amount shown above. At the same time it will reset to $1. 270 days from now, there will be another floating rate payment, and the $1 principal is returned. How does this floating rate payment not have a present value which appears in our calculations of the value of the floating rate note!?!?

e.g. look at it from the perspective of someone holding the floating rate note. If I don't sell the bond, I know that I'm going to get $xxx in 90 days, and then $xxx + principal in 270 days. Regardless of how you think of the bond paying back then reissuing at par, how does this reduce the value of that second cash flow to zero?



Edited 1 time(s). Last edit at Monday, April 5, 2010 at 10:58PM by calgaryeng123.

profil

Job great post. Made my life much easier.

ryanlb

Right , w.r.t the original date the second rest is at 360 , w.r.t the current date the second reset is at 270 . Job is clearly showing that for fixed payment he is discounting the first at 90 days and the second at 270 days .

For the floating you don't need to do the 270 , because we do not know the rate yet. We'll only know the rate 90 days later. The floating rate is established at each reset date and determines the next cash flow .