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deepdish7
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OIS discounting collateralized swaps proof

May 27th, 2012, 8:31 pm

QuoteOriginally posted by: ancastQuoteOriginally posted by: deepdish7i'd rather ask, why OIS are now used for projection curves. This does not make just any sense to me (whereas using OIS for discounting makes full sense)projection curves - I mean in an interest-rate swap with 3M LIBOR quarterly floating payments. why the hell is the new general approach today to project forward cashflows using OIS curve, not the LIBOR zero curve, as it always used to be. when the cashflows will actually depend on future LIBOR rate, not on future OIS rate. this seems just very strange to me????. Who told you that, deepdish7? This is exactly what it is NOT happening now in practice, where you use 2 curves, one to disocunt and the other to project forwards.Our firm is currently in transition to differential discounting and this is what I was able to understand so far from the presentation (though information there is scarce).If it's not OIS curve which is used for projections, what is it then?
 
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list
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Joined: October 26th, 2005, 2:08 pm

OIS discounting collateralized swaps proof

May 28th, 2012, 2:02 am

deepdish7 "Our firm is currently in transition to differential discounting and this is what I was able to understand so far from the presentation (though information there is scarce).If it's not OIS curve which is used for projections, what is it then? "It is not everything clear in this business. Nevertheless as far as pricing CSA will depend on collateral during lifetime of the contract and collateral posted say each day get a collateral interest which links to FedFund rate it might make sense to use it for forward projection. How it will be used as a discount rate from expiration day or from the current moment depends on a model.
 
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pimpel
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OIS discounting collateralized swaps proof

May 28th, 2012, 6:56 am

QuoteOriginally posted by: deepdish7QuoteOriginally posted by: ancastQuoteOriginally posted by: deepdish7i'd rather ask, why OIS are now used for projection curves. This does not make just any sense to me (whereas using OIS for discounting makes full sense)projection curves - I mean in an interest-rate swap with 3M LIBOR quarterly floating payments. why the hell is the new general approach today to project forward cashflows using OIS curve, not the LIBOR zero curve, as it always used to be. when the cashflows will actually depend on future LIBOR rate, not on future OIS rate. this seems just very strange to me????. Who told you that, deepdish7? This is exactly what it is NOT happening now in practice, where you use 2 curves, one to disocunt and the other to project forwards.Our firm is currently in transition to differential discounting and this is what I was able to understand so far from the presentation (though information there is scarce).If it's not OIS curve which is used for projections, what is it then?Projection curves are stripped from IR futures and IRS rates assuming discounting with OIS. The way you strip forwards is to make sure, that your IRS value dealt at market rate is nil.
 
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deepdish7
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OIS discounting collateralized swaps proof

May 28th, 2012, 7:00 am

QuoteOriginally posted by: pimpelProjection curves are stripped from IR futures and IRS rates assuming discounting with OIS. The way you strip forwards is to make sure, that your IRS value dealt at market rate is nil.this is what I would imagine in the first place (or using FRAs for projecting as alternative to IR futures and swaps) but I was told that projection curve will be based on overnight index swaps (which doesn't make any sense to me). i checked two times and was told same. maybe people in the bank are just mixing things up in the transition process. will recheck
Last edited by deepdish7 on May 27th, 2012, 10:00 pm, edited 1 time in total.
 
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pimpel
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OIS discounting collateralized swaps proof

May 28th, 2012, 7:06 am

QuoteOriginally posted by: deepdish7QuoteOriginally posted by: pimpelProjection curves are stripped from IR futures and IRS rates assuming discounting with OIS. The way you strip forwards is to make sure, that your IRS value dealt at market rate is nil.this is what I would imagine in the first place (or using FRAs for projecting as alternative to IR futures and swaps) but I was told that projection curve will be based on overnight index swaps (which doesn't make any sense to me). i checked two times and was told same. maybe people in the bank are just mixing things up in the transition process. will recheckI would expect the projection curve being set up as OIS curve plus basis spread. Maybe that was what they meant. In order to make life more practical I heard that the most comfortable option is to define most liquid projection curve as rates, since that is what you trade and hedge with, and OIS (discounting curve) is defined as the projection curve less the spread, since it has smaller impact on values.
 
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tula
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OIS discounting collateralized swaps proof

May 29th, 2012, 6:14 pm

QuoteOriginally posted by: pimpelI would expect the projection curve being set up as OIS curve plus basis spread. Maybe that was what they meant. In order to make life more practical I heard that the most comfortable option is to define most liquid projection curve as rates, since that is what you trade and hedge with, and OIS (discounting curve) is defined as the projection curve less the spread, since it has smaller impact on values.Agree -- it is basically a question of how you want to view your risks (ie as outright risks or as spread risks)
 
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deepdish7
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OIS discounting collateralized swaps proof

May 29th, 2012, 9:51 pm

QuoteOriginally posted by: pimpelQuoteOriginally posted by: deepdish7QuoteOriginally posted by: pimpelProjection curves are stripped from IR futures and IRS rates assuming discounting with OIS. The way you strip forwards is to make sure, that your IRS value dealt at market rate is nil.this is what I would imagine in the first place (or using FRAs for projecting as alternative to IR futures and swaps) but I was told that projection curve will be based on overnight index swaps (which doesn't make any sense to me). i checked two times and was told same. maybe people in the bank are just mixing things up in the transition process. will recheckI would expect the projection curve being set up as OIS curve plus basis spread. Maybe that was what they meant. In order to make life more practical I heard that the most comfortable option is to define most liquid projection curve as rates, since that is what you trade and hedge with, and OIS (discounting curve) is defined as the projection curve less the spread, since it has smaller impact on values.To define projection curve as rates - you mean as FRA/IR Futures/Swaps? But are they really more liquid than OIS? And isn't it better to have a single benchmark curve (OIS) rather than several rates curves which you must somehow choose between? And how would you define the spread to arrive from FRA/IR Futures/Swaps to OIS then? I'm hearing that OIS will be used as a base curve in our firm, as it's the most liquid curve..
Last edited by deepdish7 on May 29th, 2012, 10:00 pm, edited 1 time in total.
 
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pimpel
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OIS discounting collateralized swaps proof

May 30th, 2012, 6:47 am

QuoteOriginally posted by: deepdish7QuoteOriginally posted by: pimpelQuoteOriginally posted by: deepdish7QuoteOriginally posted by: pimpelProjection curves are stripped from IR futures and IRS rates assuming discounting with OIS. The way you strip forwards is to make sure, that your IRS value dealt at market rate is nil.this is what I would imagine in the first place (or using FRAs for projecting as alternative to IR futures and swaps) but I was told that projection curve will be based on overnight index swaps (which doesn't make any sense to me). i checked two times and was told same. maybe people in the bank are just mixing things up in the transition process. will recheckI would expect the projection curve being set up as OIS curve plus basis spread. Maybe that was what they meant. In order to make life more practical I heard that the most comfortable option is to define most liquid projection curve as rates, since that is what you trade and hedge with, and OIS (discounting curve) is defined as the projection curve less the spread, since it has smaller impact on values.To define projection curve as rates - you mean as FRA/IR Futures/Swaps? But are they really more liquid than OIS? And isn't it better to have a single benchmark curve (OIS) rather than several rates curves which you must somehow choose between? And how would you define the spread to arrive from FRA/IR Futures/Swaps to OIS then? I'm hearing that OIS will be used as a base curve in our firm, as it's the most liquid curve..I am not a market expert and never did a single trade, but to my knowledge, IR futures are the most liquid instruments on this planet, that is why I would set up projection curve based on those rates, and all the other curves as spread to this curve to omit problems arising from interpolation algorithms shown in "Two curves, one price". The fact you use OIS rates in bootstrapping the discount curve, does not mean, that you can not set it up later as a spread to projection curve in your system.
 
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deepdish7
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OIS discounting collateralized swaps proof

May 30th, 2012, 6:56 pm

QuoteOriginally posted by: pimpelI am not a market expert and never did a single trade, but to my knowledge, IR futures are the most liquid instruments on this planet, that is why I would set up projection curve based on those rates, and all the other curves as spread to this curve to omit problems arising from interpolation algorithms shown in "Two curves, one price". The fact you use OIS rates in bootstrapping the discount curve, does not mean, that you can not set it up later as a spread to projection curve in your system.in any case nobody was able yet to explain how to calculate the spread to OIS if we start from Rates.(
 
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bearish
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OIS discounting collateralized swaps proof

May 31st, 2012, 12:44 am

Are you challenging list for supremacy in spreading confusion around here?
 
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deepdish7
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OIS discounting collateralized swaps proof

May 31st, 2012, 2:29 pm

I am not, as nobody was able to provide any explanation on how to calculate the spread to OIS if we start from Rates and don't use OIS curve. So in the first place I don't have anything to challenge yet
Last edited by deepdish7 on May 30th, 2012, 10:00 pm, edited 1 time in total.
 
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bearish
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OIS discounting collateralized swaps proof

June 1st, 2012, 2:03 am

OK - I'll try once. So the starting point is that you have a set of swaps whose floating leg payments are based on future Libor sets. We also, for reasons we may suppress for now, agree that the proper overnight discounting rate is Fed funds. We also have a set of swaps for a few maturities whose floating leg payments are based on Fed funds (these would be the OIS swaps), and we have longer dated swaps that are based on swapping Fed funds for 3 month Libor. Taken together with the basic Libor swaps, the latter can be re-interpreted as swapping Fed funds for fixed. Step one is to fit an OIS curve to these swap rates. This can be done in any of the traditional ways we have been doing swap curve fitting. With this curve in hand, we can go on and recursively fit the forward Libor sets that will make each on-market Libor swap price back to par, under the assumption that we discount both the fixed and floating leg payments at the OIS curve. None of this is particularly hard to do. And when we have the final results, it is very easy to express one curve as a spread to the other. I agree that even if we deem the OIS curve to be the "risk free discounting curve", you may still want to hedge your short to medium maturity interest rate risk with ED futures and your long term rate risk with Libor swaps, but in order to do this you need to make some sort of assumption on how the spread between the OIS and Libor curves will change with the level of the curves.
 
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deepdish7
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Joined: October 16th, 2010, 6:57 pm

OIS discounting collateralized swaps proof

June 1st, 2012, 9:46 am

Well yes but then we use both curves - OIS and Rates (whatever it is, IR futures, FRAs or swaps). I had understanding from what some people below were saying, that we'd rather use some rates curve and ignore OIS curve completely, as it's less liquid. In that case I was wondering how can one come up with some spread if we omit OIS curve, that's what I was asking. Obviously if one uses inputs from both markets then discovering spread between them is pretty straight-forward
Last edited by deepdish7 on June 1st, 2012, 10:00 pm, edited 1 time in total.
 
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BerndSchmitz
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OIS discounting collateralized swaps proof

March 13th, 2013, 7:25 am

probably a little late for a reply but I wanted to clarify some things that kept me busy (and irritated) for some time.I have often read that collateralized swaps are discounted with ois because this is a good proxy for the risk-free rate. This argumentation is completely wrong. If the CSA would specify some other rate (e.g. 3m Libor) as the collateral rate, then this would be the appropriate discount rate - even if it happened not to be risk-free. As it turns out, even in a world without any credit risk, the collateralized swap should be valued differently from its uncollateralized counterpart. This difference stems from an expected funding benefit/costs caused by the collateralization process (LVA).Below I attached an example of 12m-tenor swaps for different maturities. It is assumed that there is no collateral risk and that all market participants agree on the same (risk-neutrally) expected forward Libors (B4:B10). Further there are some given continious collateral and funding rates (B14:B23 and H14:H23). In B27:B29 and H27:H29 I calculated the swapRates using either the collateral or the funding curve as discount factors. Not surprisingly they are different and for 2y and 3y I tried to explain the deviations (as given in B30 or B34). As you can see in B31 or B35, the difference is just the expected funding benefit (I considered a payer swap which is expected to build up a positive PV - as long as the rate structure is not inverse).The nice result is that two banks with different funding rate agree on the same swapRate for the collateralized swap. Without collateral (again assuming no credit risk) the banks would consider different swapRates to be fair. However, they also value the expected funding benefit/costs to be differently (as they have different funding spreads). It turns out that the sum of these two effects is always the same - independent of the funding rate.
Attachments
CollateralizedSwapExample.zip
(12.56 KiB) Downloaded 5 times
Last edited by BerndSchmitz on March 12th, 2013, 11:00 pm, edited 1 time in total.
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