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Topic Title: Bloomberg swap curves
Created On Wed May 30, 12 02:40 AM
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quanteric
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Wed May 30, 12 02:40 AM
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Hi, I am wondering if you can help me out with a few Bloomberg curves...

1. AUD, I understand that the convention for swaps is quarterly to 3y and semiannual from 4y onwards. When I see the AUD 6m curve from Bloomberg (curve 302), I see they use deposits up to 6m and then semiannual swaps. However, for the 1-3y points, I see that they "artifically constructed" semiannual swaps from: Q+B+Q*Q/8 where Q is the rate for the quarterly swap and B is the 3mv6m basis. I am wondering if you can help me out with the theory behind this construction?
When we get to the AUD 3m curve (curve 303), the curve is built from deposits up to 3m, rates futures up to 2y, quarterly swaps for 2-3y, and semiannual swaps from 4y onwards with the construction: S-B-S*S/8.

2. USD OIS curve.

I see that the Bloomberg USD OIS curve (curve 42) consists of OIS quotes up to 5y and from 7y onwards are constructed from a rather complex construction. I am wondering if anyone knows the theory behind it?

Thanks....
 
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Martinghoul
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Wed May 30, 12 08:37 AM
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1. There's no theory. It's all ad hoc and everyone does whatever they feel like, BBG included.

2. US FF OIS used to not trade past 5y (and, in reality, even 2y). As a result, people used to infer OIS rates past the cutoff by looking at vanilla IRS and the FF/LIBOR basis swap mkts. Strictly speaking, it's no longer really necessary, as full OIS curves are now published, as far as I can see. Again, what BBG is doing is known only to BBG.

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"Insofar as I may be heard by anything, which may or may not care what I say, I ask, if it matters, that you be forgiven for anything you may have done or failed to do which requires forgiveness."
 
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rmax
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Wed May 30, 12 09:09 AM
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Quote

Originally posted by: Martinghoul
2. US FF OIS used to not trade past 5y (and, in reality, even 2y). As a result, people used to infer OIS rates past the cutoff by looking at vanilla IRS and the FF/LIBOR basis swap mkts. Strictly speaking, it's no longer really necessary, as full OIS curves are now published, as far as I can see. Again, what BBG is doing is known only to BBG.


Is there any liquidity in the long dates post FF - LIBOR spread and the cute new world of Collateral and OIS pricing?
 
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pimpel
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Wed May 30, 12 10:12 AM
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Quote

Originally posted by: Martinghoul
1. There's no theory. It's all ad hoc and everyone does whatever they feel like, BBG included.

2. US FF OIS used to not trade past 5y (and, in reality, even 2y). As a result, people used to infer OIS rates past the cutoff by looking at vanilla IRS and the FF/LIBOR basis swap mkts. Strictly speaking, it's no longer really necessary, as full OIS curves are now published, as far as I can see. Again, what BBG is doing is known only to BBG.


When constructing OIS forward rates from FF swaps, do people bother with the fact, that the forward OIS would be equal to geometric average of over night forwards, whereas the rate paid in FF swap is an arithmetic one? Is there any simple adjustment to be made? Is the effect material?
 
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Martinghoul
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Wed May 30, 12 10:48 AM
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Quote

Originally posted by: pimpel
When constructing OIS forward rates from FF swaps, do people bother with the fact, that the forward OIS would be equal to geometric average of over night forwards, whereas the rate paid in FF swap is an arithmetic one? Is there any simple adjustment to be made? Is the effect material?

Whether people do it or not depends on their exact degree of A-R ("anal retentiveness") and their resource constraints. I don't know of any "simple" adjustment and the effect is reasonably material, given the level of liquidity.
Quote

Originally posted by: rmax
Is there any liquidity in the long dates post FF - LIBOR spread and the cute new world of Collateral and OIS pricing?

Yeah, I think there's liquidity, although it's been a while since I last got involved in the long end stuff.

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"Insofar as I may be heard by anything, which may or may not care what I say, I ask, if it matters, that you be forgiven for anything you may have done or failed to do which requires forgiveness."
 
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list
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Wed May 30, 12 10:51 AM
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see that the Bloomberg USD OIS curve (curve 42) consists of OIS quotes up to 5y and from 7y onwards are constructed from a rather complex construction. I am wondering if anyone knows the theory behind it?
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I have a feeling that construction of the OIS is a trick. Primary and the 1st step is developing floating leg of the OIS. How to calculate the day valued geometric average based on a broadly extended data of the forward rate. For example in more simpler setting we have a spot FF rate r ( 0 , 5 ), where 0=today Monday , 5= closest Friday. There are 2 ways for construction. We can solve the equation for geometric average which for given 5 days presents the same return as r ( 0 , 5 ) and the second way. It is a tricky one. We use r ( 0 , 5 ) for a day and calculate its geometric average. The second way represents something that at certain degree different than initially FF defined r ( 0 , 5 ). I could be mistaken but my intuition suggests that the second approach was chosen for the construction of geometric average day compounded floating rate of the OIS.

When we prove in calculus existence of the limit of the sequence ( 1 + r / n ) ^n it was proved that this sequence is monotonic increasing. For n = 1 it relates to simple interest rate r over say [ 0 , T ]. This interval can be split into months , weeks, or days and compounded interest corresponds to geometric average. If r is the simple interest for next 5 days then indeed each day have interest 'r' and no one can prohibit to calculate compounded rate over the same period and calculated swap rate over the same period. Thus starting with the fixed rate r ( 0 , 5 ) over [ 0 , 5 ] we arrive at other fixed rate that can be called here OIS if it is drawn from FF rate. This OIS would be higher than r ( 0 , 5 ) and investor buying fixed payed more

Edited: Wed May 30, 12 at 04:34 PM by list
 
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chilun
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Sun Jun 17, 12 07:31 AM
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Here's what I think / guess for 1). Using your convention Q, B and S...

For receiving BBSW 3M quarterly, you have pay fixed payment Q quarterly.

For receiving BBSW 6M semi-annually, you have to pay fixed payment Q quarterly together with fixed payment B semi-annually.

To unify all payment to be semiannually, you need to convert the quarterly payment Q into semiannually. Using the approximation:

POWER(1 + Q/4, 4) = POWER(1 + S/2, 2)
=> POWER(1 + Q/4, 2) = POWER(1+ S/2, 1)
=> 1 + 2 x 1 x Q/4 + Q/4 * Q/4 = 1 + S/2
=> Q + Q x Q / 8 = S

Restate...

For receiving BBSW 6M semi-annually, you have to pay (approximately) Q + Q x Q / 8 + B semi-annually. Similar things for AUD 3M curve but require even more approx.

Did not really pay attention to Bloomberg USD OIS curve. Will have a look if I have time (no guarantee).
 
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irishnoel
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Wed Jul 18, 12 09:48 PM
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the simply take the spread of the basis curve of 3$Libor vs FedFunds for each tenor point on the back end (implied fed funds) and strip this from the corrresponding swap rate:

so for the 30yr:

USSWAP30 - USBG30

Of course they adjust for the differening day count conventions ( swap is S/A 30/360) - the standard Libor curve vs Basis curve having A/360 Quarterly.

100*(100*(-USSWAP30/100+(((1.0 + ((1.0 + ((((1.0 + USSWAP30/100*(360.0/365.0)/2.0)^(2.0/4.0) - 1.0) * 4.0)-USBG30/10000)/4.0)^4.0 - 1.0)/360.0)^90.0 - 1.0) * 4.0)))

Lots of topics on this, both on bloomberg and on web. Talks of trying to make this market more liquid as the move to OIS is a concern to a lot of banks....say portfolio of WAM of 20 yrs - the spread is approx 20bps - so 20bps*DV01 is a lot of collateral that may have to be posted.
 
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