Hi, I am wondering if you can help me out with two questions on OIS discounting.1. Comparison of projection ratesUnder OIS discounting, we would get a different set of forward projection rates assuming the same set of observations. Is this an inconsistency as then we would be valuing a swap using different forward projections depending on whether it is collaterialised or not.2. Countries without OISsFor countries without OIS swaps, say South Africa. How can one go about handling collaterialised swaps or "engineer" a synthetic OIS curve?Thank you very much for your attention and help on this..

QuoteOriginally posted by: quantericHi, I am wondering if you can help me out with two questions on OIS discounting.1. Comparison of projection ratesUnder OIS discounting, we would get a different set of forward projection rates assuming the same set of observations. Is this an inconsistency as then we would be valuing a swap using different forward projections depending on whether it is collaterialised or not.2. Countries without OISsFor countries without OIS swaps, say South Africa. How can one go about handling collaterialised swaps or "engineer" a synthetic OIS curve?Thank you very much for your attention and help on this..In answer to question 2. If the swaps are collateralised in USD, then you don't need a local OIS curve. All you need is a local IRS curve + cross currency curve, and you can bring the discounting back to USD OIS. The same applies to constructing forward projection rates - one would simply have to bootstrap the curve under the assumption that all cash-flows are discounted back to USD OIS (known as dual-bootstrapping). Your synthetic ZAR OIS curve will then be an 'OIS cross currency curve', and would be built from (ZAR 3s IRS) + (USDZAR 3s xccy) - (USD 3s/OIS basis). Hope this helps.

I thought forward projections used different rates from the PVing under a CSA like scenario...??

Thanks guys. I understand that if collateral is in USD, we could do indirect via bootstrapping an implied cross-currency OIS discount curve. However, what if the collateral is in its local currency?

In response to 1. It helps if you think about changing the discounting curve as changing the currency. Then the forward rates would have to be different. But in this case the spot FX is always fixed to 1.0. See Bianchetti's paper "two curves one price" http://ssrn.com/abstract=1334356.

QuoteOriginally posted by: thedocQuoteOriginally posted by: quantericHi, I am wondering if you can help me out with two questions on OIS discounting.1. Comparison of projection ratesUnder OIS discounting, we would get a different set of forward projection rates assuming the same set of observations. Is this an inconsistency as then we would be valuing a swap using different forward projections depending on whether it is collaterialised or not.2. Countries without OISsFor countries without OIS swaps, say South Africa. How can one go about handling collaterialised swaps or "engineer" a synthetic OIS curve?Thank you very much for your attention and help on this..In answer to question 2. If the swaps are collateralised in USD, then you don't need a local OIS curve. All you need is a local IRS curve + cross currency curve, and you can bring the discounting back to USD OIS. The same applies to constructing forward projection rates - one would simply have to bootstrap the curve under the assumption that all cash-flows are discounted back to USD OIS (known as dual-bootstrapping). Your synthetic ZAR OIS curve will then be an 'OIS cross currency curve', and would be built from (ZAR 3s IRS) + (USDZAR 3s xccy) - (USD 3s/OIS basis). Hope this helps.In such approach you price at 0 all the PAR IRS trades. When you switch to EUR collateral, would you create a new projection curve? I would assume, that there is only one expectation of forward rates and if you switch collateral currency, PAR rates should be different, to reflect of different cost of collateral in different currencies. How to determine which discounting curve should be used as a default for determination of projection curve representing market expectation of forward rates? depending on market access, various players have different financing costs in different currencies.

Question 1:You have to ask yourself (or your trader or broker) under which conditions the swap rates are quoted. If the swap rates are calculated under OIS discounting (ie. assuming a cash CSA), you must bootstrap your projection under OIS discounting to get the providers view on the future fixings.You could extract a LIBOR projection (and discount) curve by bootstrapping the old way, but then its like the Black Scholes option pricing formula: You get a number/curve, but it has no direct interpretation as the assumptions are wrong. Its not completely useless, as it does give the correct par rates. But that's it.Going to pricing of the uncollateralised trades I would use as first step my projection curve calculated under OIS discounting (Some would adjust it to account for the numeraire change) and discount the cashflows with my funding curve which is different from OIS. So conceptually the same projection curve, new price because of different discounting/funding.And then there are all the extras: CVA, DVA and FVA, that should also have an effect. There is a lot going on with regard to these issues, just take a look in the General ForumQuestion 2:For contracts collateralised in other currencies, I agree with thedoc.For contracts collateralised in local currency and with no OIS market:Sorry, you have to construct the curve yourself. We have the same problem in Denmark (local currency DKK), where OIS swaps are only available for a maximum of 2 years. Our trades are collateralised in EUR, but we still construct a long DKK OIS curve. I've seen different approaches: Either spreading to the EONIA curve (EUR OIS) with a view on the spreads for the longer maturities, or assuming the same spread between OIS and 3M curve in DKK as in EUR.

QuoteOriginally posted by: KommakulQuestion 1:Going to pricing of the uncollateralised trades I would use as first step my projection curve calculated under OIS discounting (Some would adjust it to account for the numeraire change) and discount the cashflows with my funding curve which is different from OIS. So conceptually the same projection curve, new price because of different discounting/funding.And then there are all the extras: CVA, DVA and FVA, that should also have an effect. There is a lot going on with regard to these issues, just take a look in the General ForumFollowing recent papers by Castagna and Brigo, I would disagree with the above. The discounting curve should always be OIS (or xccy if collateralized in foreign currency). You include funding premium externally when determining FVA.QuoteOriginally posted by: KommakulQuestion 1:Question 2:For contracts collateralised in other currencies, I agree with thedoc.For contracts collateralised in local currency and with no OIS market:Sorry, you have to construct the curve yourself. We have the same problem in Denmark (local currency DKK), where OIS swaps are only available for a maximum of 2 years. Our trades are collateralised in EUR, but we still construct a long DKK OIS curve. I've seen different approaches: Either spreading to the EONIA curve (EUR OIS) with a view on the spreads for the longer maturities, or assuming the same spread between OIS and 3M curve in DKK as in EUR.I have similar issue, maybe slightly different currency, but also highly connected with EUR. Initially I thought about going the same way as you do, but I don't think traders assume OIS discounting when thinking about future fixings. Foreign dealers clear through LCH.Clearnet which uses Libor discounting. Local dealers are not sophisticated enough, to assume OIS discounting. The problem is, that since a lot of trades is collateralized in EUR, most of them would have non-zero NPV at inception even if traded at market rate, that is why I decided to suggest projection curve assuming xccy curve to EUR.I guess as long there is no evolution in methodologies, there is no right approach.

Thanks guys... I am wondering the swap rates we see quoted in Bloomberg, do you know if they are collateralised or uncollateralised?

QuoteOriginally posted by: quantericThanks guys... I am wondering the swap rates we see quoted in Bloomberg, do you know if they are collateralised or uncollateralised?Those from broer pages in major currencies you can assume collateralization for sure

Thanks pimpel, so the Bloomberg generic swap rate tickers for the major currencies are almost certain to be quoted on a collateralised basis? And for the minor currencies it may not be the case?

I guess that most of the quotes are collateralized, but in case of minor currencies collateral currency may be in foreign currency.

Convention for pretty much all liquid mkts is collateralized, using the same ccy collateral, like pimpel said.

QuoteOriginally posted by: pimpelI would assume, that there is only one expectation of forward rates and if you switch collateral currency, PAR rates should be different, to reflect of different cost of collateral in different currencies. You are correct. You can be quoted different PAR rates in the market, depending on what collateral agreements you have in place with various counterparties. These different rates should (in theory) lead back to the same projection curve when you feed them into your bootstrapper.

Maybe it could be of some help the note I wrote about the problem of collateral posted in a different currrency. You'll find it here.I considered also the case of CCS in the end of the paper.In theory collateral should not play a role in determining the par swap rate, which should be independent from the collateral currency (the valuation IS, instread). This is at least what comes out from the inspection. I do not agree with thedoc, since the projection curve will change if the collateral is different, although the par swap rate should be the same. The difference will be nil only of the basis of the CCSs in zero. Anyway, you can read the results in the paper. If you are not interested in equity styll contracts, you can skip the first ten-ish pages.