got you, but... in my understanding: mark at your own funding curve means (neglecting counterparty CVA i.e. assuming full collaterization) assuming that a future (from my point of view) positive cashflow has to be discounted by OIS + funding spread (since if I want to "transform" the future cash flow into cash today, I have to pay OIS+funding on this cash) and a future negative cashflow has to be discounted by OIS (for an analogous reason and OIS is the rate at which I can invest money riskless). This is not a liquidation / market value, but a cash flow management value, which is dependent on my own funding costs. There is quite a good and detailed paper on this by Fries available. Hope, I put it right here, the whole thing is always a bit confusing.Anyway. If you want to mark a plain vanilla swap at your funding curve in this sense, you can not do this by just exchanging the discount curve, because dependent on the sign of future netted cashflows you have to use different discount curves.Also, even if you replace the OIS curve by your discount curve, the quanto-like convexity correction for the libor forward comes from the OIS / Libor curve relationship, not from the funding curve. So it is still correct to induce the convexity from the OIS curve.does that make sense?

QuoteOriginally posted by: pcaspersgot you, but... in my understanding: mark at your own funding curve means (neglecting counterparty CVA i.e. assuming full collaterization) assuming that a future (from my point of view) positive cashflow has to be discounted by OIS + funding spread (since if I want to "transform" the future cash flow into cash today, I have to pay OIS+funding on this cash) and a future negative cashflow has to be discounted by OIS (for an analogous reason and OIS is the rate at which I can invest money riskless). This is not a liquidation / market value, but a cash flow management value, which is dependent on my own funding costs. There is quite a good and detailed paper on this by Fries available. Hope, I put it right here, the whole thing is always a bit confusing.Anyway. If you want to mark a plain vanilla swap at your funding curve in this sense, you can not do this by just exchanging the discount curve, because dependent on the sign of future netted cashflows you have to use different discount curves.Also, even if you replace the OIS curve by your discount curve, the quanto-like convexity correction for the libor forward comes from the OIS / Libor curve relationship, not from the funding curve. So it is still correct to induce the convexity from the OIS curve.does that make sense?Credit default is reflected in CVA calculation, which is separately done somewhere else (usually). For a more general model, you would have both funding and credit default calculated at the same time, which would reflect the right replication of default/non-default/self-default cashflows, and therefore the right economics and liquidation/market value.

yes, agreed. just wanted to explain what my understanding of "marking to the funding curve" is and stress that computing CVA is not part of the following. So talking about full collaterization (i.e. no CVA anywhere) and changing from OIS to another discount curve, the main point I wanted to say wasQuotequanto-like convexity correction for the libor forward comes from the OIS / Libor curve relationship, not from the funding curve. So it is still correct to induce the convexity from the OIS curve.therefore I think it is no disadvantage to use approach 2a (include convexity in the estimation curve) compared to 2b (compute explicit convexity adjustment)second point was, that marking to the funding curve (still without CVAs) is not as easy as to just replace OIS by the funding curve.Independet of that. Question. Marking to funding for non collaterized deals means combining this with cpty CVA (no own CVA). Computing the full market value / liquidation value for non collaterized deals means computing cpty and own CVA, but no marking to own funding curve. Correct?

QuoteOriginally posted by: pcaspersIndependet of that. Question. Marking to funding for non collaterized deals means combining this with cpty CVA (no own CVA). Computing the full market value / liquidation value for non collaterized deals means computing cpty and own CVA, but no marking to own funding curve. Correct?Practically there are different ways of looking at this. The results are not equivalent and practically people ignore them. From fair value point of view, you would want to collect all default values in all scenarios as your bi-lateral CVA, whether cpty or own default. You could apply different discounting for positive and negative cashflows. That is assuming that both cpty and own defaults traded liquidly in the market place and all future possible cashflows can be replicated there.As you pointed out, people could mark to funding curve and combine with cpty CVA, this is to say that all values to you are reflected in your funding market. The cpty default will result in some loss in those values, therefore the cpty CVA.

Again, in an attempt to summarise everyting would this be a fair assessment?I pay 3mth LIBOR vs receiving fixed swap with a counterparty with a CSA...I use my 3mth basis curves to for project the float side of the swap. The two cash flow streams are then discounted using OIS. The inception value of the swap will be 0, as time moves forward the valuation will change...when positive NPV in my favour the counterparty will post me collateral equivalent to the NPV and I will pay them OIS on the collateral and vice versa. Assuming this is a fair summary, my questions now relate to non-CSA counterparties. If this is not correct could you point me in a more correct direction.Okay, now to a counterparty with no CSA?We still have the same swap, i.e., I pay 3mth LIBOR vs receiving fixed.When using my basis curves to project 3mth LIBOR do I incorporate a spread onto the forward curve so as to make it a par swap at inception? If so, depending on the time horizon of the swap I assume that the spread would not be flat but at different points in time there will be increasing spreads attached to reflect great uncertainty as you go further out in time?I will discount using a credit spread adjusted OIS curve to calculate the present value of the swap.If I don?t include a spread on my forward curve and I discount using my credit adjusted OIS curve then I won?t have a par value spread at inception, is this a fair assumption?Or should the forward curve be the same for both CSA and non-CSA counterparties and the spread is added to the fixed side so that I can have an ATM swap valuation at inception? In an ideal world my own credit rating should enter the equation too when calculating the valuation of the swap?Would it be fair to say that by adding in the credit spread on to the OIS discounting curve that implicitly I am making a Credit Valuation Adjustment (CVA) and therefore I do not need to make the calculation external of the swap valuation?If this is repeating previous posts, I apologise, but I am merely trying to draw a lot of different strands together so have a coherent summary of the issues clear in my own head.Thanks.

How are you going to estimate your credit spreads? Are you then going to have a different curve per counterparty? I think this is unpractical and when it comes to agreeing collateral settlements when you use OIS or Libor on your curve really doesn't matter. Libor is pretty standard practise for the purpose of valuations still so when it comes to posting collateral two parties can come to an agreement normally with the help of a third party servicer. Whatever happens its not an exact science and you dont need this much detail when it comes to valuation, or trading because of bid/ask spread and transaction costs

Use CDS or bond spreads to adjust your projection curves and then adjust your OIS for discounting.Yes, this would imply the use of a different curve for each counterparty. It might not be a practical solution but it would be the most correct method of adjusting valuations based on your counterparty's and your own default risk. At least this is what I am trying allude to with respect to my previous post and I am looking for feedback on my assumptions.Of course if they have a CSA in place then they are treated pretty much the same in terms of valuation as you have collateral against the valuation of the swap, however, I would argue that there is a big difference in the valuation of your swap depending on weather your counterparty is a AAA sovereign or a CCC corporate if they are non-CSA...LIBOR was standard practice for swap valuation but that has now switched to OIS for CSA counterparties. For non-CSA counterparties it should be your own funding curve...for non-CSA counterparties I am wondering if it is correct/ideal practice to discount using credit adjusted OIS curves.

I believe speaking about credit risk in swaps is a waste of time when you enter a swap agreement with a conterparty where ...1. Theres no principal changing hands2. Both parties have signed an ISDA agreement3. There is a CSA in placeWhether you use Libor or OIS is really down to personal preference. The problem with using your own funding curve in producing valuations is proving that thats you funding curve. At least if you use Libor you have a reference market rate and it completely transparent for producing financials. At the end of the day the reason you need a valuation is to evaluate your portfolio, produce financials and for posting collateral.I am taking about end of day evaluations here as appose to traded levels.

Sorry to all, I just couldn't let this beauty go.A practical question I have not yet found an answer to...Why is it correct to use 1Y swap rates vs 3M Libor on a 3M curve? When you discount the 1Y cashflows you use the Discount rate calculated from the Zero rate of the 3M futures, and the zero rates calculated from the 1Y swap rates... Would it not be more appropriate to use a 3M swap rate to build out the rest of the curve??

Hi all,I follow the following approach. Strip a purely EONIA/OIS curve from all available instruments quoted against EONIA/OIS. This is used as the discounting curve.For each Libor rate, e.g. 6M, I use 6M Libor, quoted FRAs and quoted Swap prices. For the stripping algo to build Libor Curve I use EONIA/OIS discounting. Thus, the Libor curve determine the forwards.Another way could be to add the basis swap to the EONIA/OIS rates and get the corresponding LIBOR curve.Would be very helpful if the people discussing give a hint on how they build up the OIS, 1M, 2M, ..., 6M, etc. curves and how basis curves enter the setup. Some recipes - like the one above - might be helpful to comment on that.Best, Lapsi

One question which I don't think has been adressed on this post yet is what kind of discounting curve one should use when valuing cross currency swaps. For example, take the USD leg of a cross currency swap. Does one discount cashflows using a FedFunds, or a 3m $LIBOR curve?

pcaspers, have you found any difficulty in implementing this methodolgy and pricing structures? Also, what type of cenvexity adjustment are you applying to adjust the forwards?

no, but I only tried the approach "one discount curve, several estimation curves" with implicit adjustments. I did not try to calculate separated adjustments in practice actually.