Par rate is swap rate?

CFA Level II Fixed Income
#1

I found in the Los35c and the Los35f, par rate and swap rate are calculated from spot rates with the same formula:

(1-P(0,T))/ sum( P(0,i) avec i=1,…,T)

Is it possible?

#2

Swap rate = the fixed rate that is consistent with today’s term structure of interest rates that makes the PV of fixed payments = to the PV of variable payments (again, that is as of today’s term structure). The formula you’re referencing is the quicker way to calculate what that fixed swap rate (“par”) is. Hope this helps, maybe somebody else can elaborate a little more.

#3

Thank you. This formula is for calculating the swap rate as you said.

But the par rate (maturity n) is also calculated by this formula:

(You can find the formula here https://en.wikipedia.org/wiki/Par_yield )

So, I don’t know whether par rate (par yield rate) is swap rate. :frowning:

#4

Yes, it is.

When replicating a swap with bonds, the floating-rate bond sells at par, so the fixed-rate bond has to sell at par. Thus, its coupon rate has to be the par rate.

#5

Thanks S2000magician.

I have a last question: par rate is always equal swap rate, or par rate is just equal to swap rate in some special cases?

Can we have a situation that par rate is different to swap rate?

#6

Only in special cases.

But _ all _ cases are special.

:wink:

So they’re always equal.

#7

Thank you very much, S2000magician!

#8

You’re welcome.