SWAP RATE, comfused

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2^#

发表于 2011-7-13 17:04 | 只看该作者

Par = 1
Par = PV of coupons + PV of Principal
if coupons are market coupons = swap rate (with several assumptions) (fixed rate)
coupons can be also forward rates (in case of floater)
1=PV of coupons + PV of principal

PV of coupons = 1 - PV of principal

Coupon = forward rate
PV of coupons = Sum(FDF x forward rate)
FDF = Zn = Discount factor (your formula of Zn is wrong...)
Principal = 1

swap is exchange of fixed coupons against floating coupons

PV of fixed coupons = PV of floating coupons

PV of fixed coupons = Sum(FDF x fixed coupon) = fixed coupon x Sum(FDF)

fixed coupon = swap rate = PV of floating coupons / Sum(FDF)

mar350

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3^#

发表于 2011-7-13 17:04 | 只看该作者

sorry for confusion

in my previous message, FDF=Zn=discount factor = 1/(1+Rn)^n

I might have misunderstood the meaning of FDF and Zn in your message.

Everything is valid with this in my previous message.

"I am sure that In CFA Level II: swap rate=(1-Zn)/(Z1+Z2....Zn), {Zn=Discount factor}"

here the discount factor = 1/(1+Rn)^n, where Rn is regular spot rate (not forward rate)

the idea of discounting over 1 interest period using forward rate (which probably confuses you) when pricing a floater explains why floating rate bond equals par (with simplifying assumptions)

pennyless

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4^#

发表于 2011-7-13 17:04 | 只看该作者

The way CFA level 2 and 3 calculate the swap rate is the same (although it took me a while to figure it out). I suggest not read Schweser books for that chapter because it's way to simplified and misses a lot of key information. CFAI explains swaps clearly.

jmh530

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5^#

发表于 2011-7-13 17:05 | 只看该作者

mik82 Wrote:
-------------------------------------------------------
> The way CFA level 2 and 3 calculate the swap rate
> is the same (although it took me a while to figure
> it out).

Thanks guys, can anyone point out why the way CFA level 2 and 3 calculate the swap rate is the same?

(the key point to confuse me.)

Edited 1 time(s). Last edit at Saturday, March 26, 2011 at 02:11AM by baifan.

oneboy

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6^#

发表于 2011-7-13 17:05 | 只看该作者

baifan Wrote:
>
> Thanks guys, can anyone point out why the way CFA
> level 2 and 3 calculate the swap rate is the
> same?
>
> (the key point to confuse me.)

mik82 or anyone please give me a hand, thanx.

Analyze_This

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7^#

发表于 2011-7-13 17:05 | 只看该作者

anyone help?

Analti_Calte

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8^#

发表于 2011-7-13 17:05 | 只看该作者

swap rate=(1-Zn)/(Z1+Z2....+Zn), {Zi=discount factor}
swap rate=[SUM(FDF*forwad rate)]/SUM(FDF), {FDFi=Zi(mentioned)}

==>

(swap_rate)*(Z1+Z2+....Zn)+Zn = 1
(swap_rate)*(Z1+Z2+....Zn) = Z1*forwad_rate_1+...+Zn*forwad_rate_n

==>

PV(received fixed rate counpon bond)= PV(received floating rate bond)
PV(received fixed rate coupons) = PV(received floating rate counpons)

The only difference is whether is the principal is paid or not.

Notes: forward_rate_i could be derived from the discount factor Zi's, vice versa.

Edited 2 time(s). Last edit at Monday, March 28, 2011 at 09:37AM by deriv108.

bpdulog

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9^#

发表于 2011-7-13 17:05 | 只看该作者

At issue, a floating-rate bond has par value. That is,

Z1*forwad_rate_1+...+Zn*forwad_rate_n+Zn=1.

So the swap rates in the two approaches are the same.