Hi All,I am getting confused about pricing CSA vs no-CSA swaps, so can somebody help me out?1. Without considering the CVA etc., should the par swap rate for a trade under CSA or a no-CSA the same? If not, where can I get the market quoted par swap rate for a no-CSA trade?2. For CSA and no-CSA, should we have the same forward Libor rate? Or should we re-bootstrap the forward curve if we switch from OIS to Libor discounting?Thank you so much

Last edited by kelang on March 2nd, 2012, 11:00 pm, edited 1 time in total.

- Martinghoul
**Posts:**3256**Joined:**

As far as I am aware, you have to answer this question by making a fundamental choice that everyone makes for themselves. There is no right answer.

QuoteOriginally posted by: MartinghoulAs far as I am aware, you have to answer this question by making a fundamental choice that everyone makes for themselves. There is no right answer.Thank you so much Martinghoul, I benefit quite a lot by reading your answers on many threads...Yes, I understand what you mean. But now it seems there is some inconsistency there:Let us say we have a list of market instruments (by recent market practice, it will be under OIS discounting?, hopefully...)Case I: (Assumption: the forward curve will be the same for all trades, and the forward curve is derived under OIS discounting)Given the market instruments, one constructs OIS curve and 3M forward curve (OIS)- For CSA trade, one obtains the par-swap-rate with OIS and 3M forward Curve (OIS), we are good- For the same trade but under no-CSA, one obtains the par-swap-rate with Funding Curve and 3M Forward Curve (OIS), let us say the funding curve is 3M libor. One can either use 3M Forward Curve (OIS) or re-build a 3M Libor discounting curve to be his/her funding curve. - However, in both cases, one should expect a little bps difference in the par swap rate compared with the CSA tradeCase II: (Assumption: assuming market rates for CSA and no-CSA trade are the same without considering CVA etc.)Given the market instruments, one constructs OIS curve and 3M forward curve (OIS)Given the same market instruments, one construct a Libor discounting curve and 3M forward Curve (Libor)One should NOT be surprised to see a 2-3 bps difference in the forward rate (under OIS or Libor) depending on the Libor/OIS spread and curve steepness.- For CSA trade, one obtains the par-swap-rate with OIS and 3M forward Curve (OIS), we are good- For the same trade but under no-CSA, one computes the par-swap-rate with Libor discounting curve (his/her funding curve), and 3M forward Curve (Libor)- For the two trades, since we build the curve by matching to the same set of market instruments, we expect same par-swap-rateSo hope I explain my problem. Is there some inconsistency in the two cases? getting so confused now...Thanks

Last edited by kelang on March 2nd, 2012, 11:00 pm, edited 1 time in total.

- Martinghoul
**Posts:**3256**Joined:**

Yes, so I am not entirely sure what your question might actually be. The two cases are, in fact, inconsistent.

QuoteOriginally posted by: MartinghoulYes, so I am not entirely sure what your question might actually be. The two cases are, in fact, inconsistent.Thanks Martinghoul.My key question is,First of all, most practitioners are moving to OIS, so in the OIS world, one has a discounting curve and a set of tenor forward curves. They are in principle used to price CSA trade only...Now if one has a no-CSA trade, do you think the forward curve will be the same as CSA? If not, how one can determine the forward curve for no-CSA trade?// It seems most market practitioners assume they are the same, am I right? but in principle it is wrong...// If one assumes they are the same, the par swap rate for CSA and no-CSA might differ by 0.50bps given current market condition...

Last edited by kelang on March 4th, 2012, 11:00 pm, edited 1 time in total.

hi kelangI agree with you that, in principle, forward curves depend on the particular funding assumption (ie. CSA or not; if yes, what collateral currency & rate; if not, what unsecured funding rate) that is used for calibrating the curves. This is discussed in Piterbarg's 2010 paper and to some extent (for cross currency basis swaps) also in the Fujii et al 2010 paper. In Piterbarg's model the difference between CSA and non-CSA forward rates is shown to depend on the correlation between the bank's funding spread and the underlying index / Libor rate (which makes sense intuitively).Now, I am by no means an expert in this, but I have yet to see CSA and non-CSA forward curves distinguished in practice (or even forward curves for different collateral currencies/rates). So I too would be interested to hear how other people/houses deal with this, and also about how large the difference might be (I have not done any calculations myself).cheerstula

QuoteOriginally posted by: tulahi kelangI agree with you that, in principle, forward curves depend on the particular funding assumption (ie. CSA or not; if yes, what collateral currency & rate; if not, what unsecured funding rate) that is used for calibrating the curves. This is discussed in Piterbarg's 2010 paper and to some extent (for cross currency basis swaps) also in the Fujii et al 2010 paper. In Piterbarg's model the difference between CSA and non-CSA forward rates is shown to depend on the correlation between the bank's funding spread and the underlying index / Libor rate (which makes sense intuitively).Now, I am by no means an expert in this, but I have yet to see CSA and non-CSA forward curves distinguished in practice (or even forward curves for different collateral currencies/rates). So I too would be interested to hear how other people/houses deal with this, and also about how large the difference might be (I have not done any calculations myself).cheerstulaYes, things get much complicated in nowadays. Fujii's paper seems to assume we have market-quoted for both collateralized and non-collateralized instruments if I understand correctly, then for noncollateralized trades, build funding curves and forward curves thereafter (but in fact we don't have market-quoted non-collateralized instruments...). Piterbarg's paper seems to have assume some sort of process for the spreads which is not that easy to be accepted by traders. It seems people are assuming the forward curve be the same for CSA and non-CSA trade, e.g.http://www.risk.net/risk-magazine/featu ... rice-wrong (Mis-pricing section) as per Barclays Capital's interview(Barclays Capital?s Hallett says current levels of difference between using the euro overnight index average (the OIS rate for euros) and three-month Euribor as a discount rate on par, spot-starting euro interest rates swaps is currently up to 0.65bp on the swap rate, depending on the exact tenor of the swap (with the Euribor-discounted price being lower). For off-market trades, the pricing differences can be materially greater, he says.)or, http://www.sungard.com/~/media/Campaign ... eSwap.ashx

Last edited by kelang on March 4th, 2012, 11:00 pm, edited 1 time in total.

QuoteFujii's paper seems to assume we have market-quoted for both collateralized and non-collateralized instruments if I understand correctly, then for noncollateralized trades, build funding curves and forward curves thereafter (but in fact we don't have market-quoted non-collateralized instruments...). Here they explicitly mention that separate quotes for swaps with different collateralization might not be available, so you might need to make an explicit assumption on the forward rates (eq. 3.31)QuotePiterbarg's paper seems to have assume some sort of process for the spreads which is not that easy to be accepted by traders. At least he provides a consistent theoretical framework in which the source of the difference might be understood.Thanks for the links, the second one is useful (although I disagree with some of its statements)

While there is indeed a theoretical distinction between the forward curves for different funding settings (eg, that Fujii paper mentions the forward curve will be different when using XCCY basis swaps for funding, but then turns around and says in practice it's not much different from the OIS case, so ignore it), the market consensus (by which I mean my own swaps desk... and confirmed by various conferences) is that your Libor curves are essentially invariant. For the major markets this means using the OIS and vanilla swaps (which are CSA'd) to generate your forward curves. Then when you price derivatives in a non-CSA setting (say using your own funding curve for discounting cash flows), you will use these forward curves to query Libor values. So you should definitely expect to see differences in your swap rate quotes.Anyway, that's the approach for the major currencies like USD and EUR: things can get interesting when there is no OIS market (or not interesting at all...)

What about when the collateral posted is different from the trade and settlement currency?

I'm guessing the case you mean is when you have a vanilla swap market CSA'd in a different currency. As far as curve building goes, you'll have to calibrate your XCCY basis swap market and vanilla swap market together to generate the discount and Libor curves.

My tuppence worth! Quotes observed on Bloomberg etc. are now assumed to be on the basis that both parties to the trade post cash collateral in the currency in which the trade is denominated with zero thresholds and daily posting (LCH model?) If you agree a trade with terms different from these the pricing should differ. So if you have to price a non-collateralised trade (say) you have to adjust this price to reflect the different discounting (at your marginal funding rate), a CVA charge and an adjustment for the fact that your expected hedging costs will depend upon the correlation between OIS swaps, Libor swaps (both collateralised) and the funding rate. This last factor is akin to the quanto adjustment that is made in the pricing of "diff" swaps.

- Martinghoul
**Posts:**3256**Joined:**

I agree with this, assuming "quotes" refers to par spot swap rates. I believe this is also what's used for ISDAFIX, so it's more or less the standard. And yes, I believe this is the "LCH model".

Sorry, yes by quotes I mean par swap rates. One of the interesting things about this is the issue of hedging trades that are not done on the standard terms with trades that are. In the presence of significant funding costs the notionals of non-collateralised and the hedging collateralised trade (especially for longer dated trades) can be quite different. I suspect that some mid and smaller sized banks have not yet allowed for this and consequently are running significant "delta" risk.

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