Swap Question

[Delo]

A bank entered into a 4-year tenor plain vanilla swap exactly three years ago from today. The agreements of the swap are to pay 6.5 percent annually, based on annual compounding with a 30/360 day-count convention, fixed rate on a $50 million notional, and receive 1-year London Interbank Offered Rate (LIBOR). The continuously compounded LIBOR for 1-year obligations is currently 5.75 percent. The 1-year LIBOR at the beginning of the period was 6.25 percent. The value of the swap is closest to:

• $110,000.
• -$270,000.
• $800,522.
• -$257,020.

Can anyone help me with the answer and explanation?

 

[ShaktiRathore]

Hi
Value of swap to fixed rate payer bank at end of 3rd yr=pv of net received amt at end of 4th yr
Fixed rate paid=6.5% (discrete)
Floating rate received is given continous so convert it to discrete,=exp(Rc)-1=exp(.0575)-1=5.919%[forget 6.25% its rate at begining of contract i think does not relevant pay attention to word "was" instead of "is" is used)
Value of swap=(.05919-.065)*exp(-.0575)*-50000000=-274,267 near to option b -270,000,is it correct answer?
Thanks

 

[Bester]

Hi,

I get a similar answer if I do it as follow, however it still does not make intuitively sense to me why for the calc of the floating leg, both the same underlying discrete and continues rate is used:

Fixed leg:
(6.25% * $50 000 000) + $50 000 0000 = $53 250 000 ---- cashflow at end of 4th year,
of which the PV is R50 274 490 --- using libor continues rate 5.75% for PV of the fix leg

Floating leg:
($50 000 0000 + ($50 000 000 x 5.919%),
of which the PV is $50 000 223 --- using the continues rate of 5.75% for PV of the floating leg

Therefore value of the swap is $50 000 223 - $ 50 274 490 = $274 267

Can you please assist if my understanding is wrong in the above calc.

Thanks

 

[Delo]

Yes, -$270,000 is the correct answer.

 

[Delo]

Thanks @ShaktiRathore and @Bester

But interestingly.. the answer given in source is very concise
FIXED: The value of the fixed-rate component of the swap is ($50 × 1.065)e^(-0.0575*1) = $50.27M.
FLOATING: The value of the floating-rate component of the swap is its par value of $50M since we are currently at an annual settlement date.
Hence, the value of the swap to this counterparty is approximately $50M - $50.27M = -$270,000

This particular concept of swap in confusing to me. But I guess I just have to memorize now (given exam is so close). David's notes also alludes to the same concept...See snippet from his notes



One more from GARP Practice Qs 2010:-

 

[David Harper CFA FRM]

This came up before here @ https://forum.bionicturtle.com/threads/vanilla-swap-question.3426/#post-9292
Here is my XLS referenced (please excuse the imperfect labels etc) https://www.dropbox.com/s/wyqd5912h2i3b5c/0705_swap_ammor.xlsx?dl=0

The upshot for me is that I got basically the same answer as @ShaktiRathore
... although I needed to assume that the immediate swap payment has already settled

@Bester I think you should be getting an exact $50.0 million for the floating leg, as the present value of the floating let (valued "as if" a bond) is given by:
(50 + 50*[exp(5.75%) - 1])*exp(-5.75%); i.e., par + coupon at 5.75% converted to annual then discounted at 5.75%, which is equal to:
50 * [1 + exp(5.75%) - 1] = 50; necessarily prices to par

 

[Delo]

" par + coupon at 5.75% converted to annual then discounted at 5.75%, which is equal to:
50 * [1 + exp(5.75%) - 1] = 50; necessarily prices to par"

Now I get it ! Thanks,