Hi all,I have a issue concerning the discounting for uncollateralised swaps. I know that some banks still use LIBOR discounting for these trades, while using OIS discounting for collateralised trades. This makes sense the me (whatever Hull and White say) as the LIBOR rate is close to the market funding level and fits in well with the Fujii and Takahashi framework for uncollateralised and collateralised swaps. As far as I am concerned, if one decides to use LIBOR discounting for uncollateralised trades, then one should use the vanilla LIBOR forward curve for projecting cash flows. That is, one should NOT use the Dual Curve Bootstrapped (DCB) LIBOR forward curve. The DCB curve is only applicable when using OIS discounting and reflects the expected future cash flows using the OIS discount factor as the numeraire. On the other hand the vanilla LIBOR forward rate gives the expected future cash flows using the LIBOR discount factor as the numeraire.The nice thing about this is that with the one set of swap rates, we can price par swaps at 0 under either LIBOR or OIS discounting. The problem that some people have with this is that there are essentially two sets of forward rates - one DCB and one not. Some traders I work with do not seem to like this and think that there should only be one forward curve for both collateralised and uncollateralised trades. Their view is that quoted par swap rates are collaterlised by implicit assumption and this produces the one and only forward curve. Worse, there is Bloomberg documentation out there that seems to confirm this view.So, my question is this:Do any of you still price uncollateralised swaps with LIBOR discounting? If so, do you use the DCB LIBOR curve for forwarding and/or for discounting?Thanks in advance...

You're facing a general issue that has been discussed here a few times. There're really no right answer and you just have to make a choice between the accuracy of your mark-to-market valuation and the internal consistency. If you look up an old thread titled something like "Comsistent Valuation of Swaps", you should be able to see people discussing this.

hi bazzat,I agree that in principle for each different collateral rate there should be a separate forward curve for the same LIBOR index. However, as you cannot observe quotes for uncollateralized swaps, you won't be able to calibrate an "uncollateralized LIBOR forward curve". And even if you could obtain such quotes, they would reflect your credit risk (relative to your counterparty) and would mess up things even more, I'm afraid. So in practice the "overnight-rate-collateralized LIBOR forward curve" indeed ends up being the only one.Martinghoul, do you mean this thread? I don't remember this topic coming up in previous discussions.

Yeah, that's the one. It's the same basic dilemma.

Thanks for the replies. Having dug into this a little more, as far as I can tell, most banks that use LIBOR discounting for uncollateralised swaps seem to use Dual Curve Bootstrapped forward rates and a vanilla (non-DCB) LIBOR curve for discounting, or perhaps a LIBOR curve plus a funding spread. This use of a DCB forward in the absense of OIS discounting doesn't make sense to me, as with such a valuation scheme, an uncollateralised FRN that pays LIBOR flat will have a non-zero value. How is that possible?BTW, as regards credit risk with an uncollateralised swap, this can be dealt with separately using a CVA charge (even though in practice CVA will be built into the swap rate and not charged separately). So in theory an uncollaterlised swap should have the same par swap rate as a collaterlised swap.Is it right that an uncollateralised FRN paying LIBOR flat should have a non-zero value (excluding CVA)?

"So in theory an uncollaterlised swap should have the same par swap rate as a collaterlised swap."The CVA charge, assuming it is built into the price, is a one-time upfront item. It may be right charge at the time of origination but it may not be right tomorrow or next week or next year.Collateralization, on the other hand, is an ongoing process, always keeping the deal current.While clearly related, isn't it a bit of a stretch to see these two things as being identical?

@DavidJNMy point is that credit risk is taken care of in a separate charge and is not necessarily a cause for a difference in par rates of collaterlised and uncollateralised swaps. If we exclude CVA, what is the difference between collaterlised and uncollateralised swaps? IMO the difference is just the funding cost/benfit of collateralisation. If we further assume that banks can fund at LIBOR, then the funding cost is taken account of in OIS discounting, as explained in Fujii et all (2010).I have a general issue with the claim that uncollaterlised par swap rates are completely different from collateralised par swap rates. Even if this were true, why do people think that a Dual Curve Bootstrapped LIBOR curve is the appropriate forward curve for uncollateralised swaps?The purpose of dual curve bootstrapping is to give collateralised par swaps a value of 0 under OIS discounting. Period. Why is this curve considered appropriate for projecting cash flows for uncollateralised swaps?And, again, how can we honestly say that an uncollateralised FRN paying LIBOR flat has a non-zero value (ignoring credit risk)?

I think it is fair to say that this is an unsolved problem. You have done some thinking about this. A lot of people have thought about this. There should be a simple way to test your hypothesis - do market quotes support your conjecture? Do you have a line of sight to such market data?

QuoteOriginally posted by: bazzat@DavidJNMy point is that credit risk is taken care of in a separate charge and is not necessarily a cause for a difference in par rates of collaterlised and uncollateralised swaps. If we exclude CVA, what is the difference between collaterlised and uncollateralised swaps? IMO the difference is just the funding cost/benfit of collateralisation. If we further assume that banks can fund at LIBOR, then the funding cost is taken account of in OIS discounting, as explained in Fujii et all (2010).Pardon my ignorance, but if the swap is fully collateralised why would it incur a CVA charge? I would have though its IM will be calculated using suitable stresses and closeout intervals to obviate any losses from counterparty non-performance?