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Muddahudda

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tT
发表于 2011-7-13 17:04 | 只看该作者

SWAP RATE, comfused

人生, about, reading, question
Hey All,

I have a question about reading 37. why we have different swap rate formula for interest swap in Level III from the one in CFA Level II .

In CFA Level II: swap rate=(1-Zn)/(Z1+Z2....), {Zn=1/(1+Rn)} it means that we liquadate every period. PV of one period floating payment equate entire period fixed.

While in Level III Reading 37, in Kaplan Notes, swap rate = [SUM(FDF*forwad rate)]/SUM(FDF), {FDF=Zn(mentioned)}, PV of entire period floating equate entire period fixed. I also read the fomular in book, it is almost the same, which just use Zero coupon bond instead of FDF.

Quite confused, Any one helps.

Thanks in advance for any insight,
Baifan



Edited 2 time(s). Last edit at Wednesday, March 23, 2011 at 09:09PM by baifan.

 

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zwjy

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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)

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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)

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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.

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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.

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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.

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Analyze_This

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7#
发表于 2011-7-13 17:05 | 只看该作者
anyone help?

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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.

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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.

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