FF/Libor and Libor/OIS basis swaps

quentin · January 18th, 2012, 7:13 am

Hello,I would like to know what conventions (maturities, frequencies, spread quotation, day basis...) are used for Libor vs OIS basis swaps in EUR and US markets?I found following information on Libor/FF basis swaps but am not sure whether they apply to OIS case:- 3M Libor paid quarterly- versus arithmetic average effective rate plus spread, paid quarterlywith maturities 3y to 10yPurpose is to build discount curves then multi-Libor curves.thanks!

recepyakar · January 19th, 2012, 2:48 pm

Libor/FF swap receives 3M Libor, pays latest Fed funds rate plus x bps (spread). Both legs are count on Act/360 basis and discounted with OIS swaps (a recent correction on IRS, XCCY, basis, etc..). But the forward curve to be derived for receiving led is counted on 30/360 day convention.As OIS is the generic form of geometric average of o.n. fed funds rate for a certain payment period, Libor/OIS swap should be the same with above expression. These expressions are for US market only. Just to remind, differentiation between day weights for week days and friday is crucial here.Hope this helps, i can send you an OIS swap and/or a Libor/FF swap case if you need.R

list · January 19th, 2012, 6:21 pm

My question might be not directly relates to the problem. Libor is submitted at 11.00 - 11.10 from panel banks and therefore is based on the < 11 o'clock morning information. If the other leg is a Treasury rate which rate do the use for Treasury rate , whether it is 11 morning data, or open of this day, closed or high or low or might be the previous day data or other? Whether they used ask prices against LIBOR?

kypr · January 19th, 2012, 9:20 pm

Hi all,My understanding of the FF/LIBOR swap conventions is as follows:- quarterly exchange of flows with a netting agreement in place, which means that the flows pay on the same days- ACT 360 basis on both legs- the rate on the FF side is arithmetically averaged. The averaging is weighted, i.e. the Friday rate has a weight of 3 on a "normal" week-end- there is a 2 day cut-off at the end of the averaging period- these instruments are quoted out to 30YTo answer list's remark: LIBOR fixes upfront, but the averaging goes on until nearly the end of the period. The 2 day cut-off period ensures the smooth payment transaction.@quentin: there are actually easier ways to skin the cat. There are classical OIS instruments quoted in the US market out to 30Y. If you want to build a discounting curve with FF-LIBOR spreads, then you run into a recursive curve build: to project the LIBOR rates you need the discounting rates, to compute the discounting rates you need LIBOR rates.Finally, I don't know the conventions for the EUR EONIA-EURIBOR basis swap (quentin, I'm assuming you meant EUR EURIBOR, not EUR LIBOR).

raags · February 28th, 2012, 8:38 pm

Hi,Please find attached document which has in detail discussion on different basis swaps.

quentin · March 22nd, 2012, 12:42 am

thank you raags

krishnan · July 9th, 2012, 5:55 am

I saw this stream of questions quite interesting. I was wondering if someone can help in suggesting some solutions. I was wondering how someone can hedge interest rate risk in the short end portfolio with only swaps? I would like to come out with a solution from operational perspective to hedge IRR( interest rate risk ) against non parallel shift of yield curve. I would indeed appreciate any suggestions.Cheers,Krishnan

kypr · July 9th, 2012, 7:33 am

The parallel/non-parallel shift of the yield curve depends on how you compute the risk, not really on the curve instruments.You can probably hedge the short end risk with swaps (called short swaps) if they are liquid enough; they are used in the 1m space. But regardless, even if you hedge with futures, you do not necessarily assume a parallel curve shift unless this is how you compute your risk.

mathmarc · July 9th, 2012, 9:02 am

QuoteOriginally posted by: kyprIf you want to build a discounting curve with FF-LIBOR spreads, then you run into a recursive curve build: to project the LIBOR rates you need the discounting rates, to compute the discounting rates you need LIBOR rates.In a multi-curves framework all the curves must be build concurrently. It is only by selecting some special set of instruments to build the curves that you can construct the curves one-by-one. The one-by-one curve construction is an exception, not the general case. Any decent curve calibration system will nowadays allow to build a multi-curves "package" in one step, including any liquid market instrument dependency. That is what multidimensional root finders are for. The OIS/Ibor dependency is one of the classical entanglement of curves. Other classical ones are vanilla and basis swaps interaction when not all tenors use the same conventions, in AUD in particular, and "foreign" currency curves when the cross-currency and foreign currency do not use the same tenors (like JPY with 6M swaps but 3M cross-currency to USD).

kypr · July 9th, 2012, 10:33 pm

Yes there are cases where you have to use the global solver, whether it is a rule is debatable. Agreed about AUD, but USD/JPY and similar cases are subject to your modelling choices. You can build single currency JPY projection curves (3m, 6m...) independently as long as the JPY discounting curve does not depend on them and they don't depend on each other.

mathmarc · July 10th, 2012, 11:32 am

QuoteOriginally posted by: kypr You can build single currency JPY projection curves (3m, 6m...) independently as long as the JPY discounting curve does not depend on them and they don't depend on each other.If you build JPY curves with OIS JPY discounting I agree with you. The example I had in mind was building the JPY discounting from FX swaps, cross currency swaps (USDLIBOR3M/JPYLIBOR3M). For Libor swaps in JPY, the standard is fixed/JPYLIBOR6M; so you have to use JPYLIBOR3M+spread/JPYLIBOR6M to finish the circle. The instruments used in discounting curve depend on JPYLIBOR3M, the ones in 3m curve depend on discounting and JPYLIBOR6M and the ones in 6m depends on discounting.

jschnaz · July 10th, 2012, 5:55 pm

Wouldn't this be the case only if JPY interbank swaps were collateralised in USD?The need for "global solving" exists but in practice I only know of the following cases, and most of them involve only 2 curves:- USD, if you put OIS/3M swaps on the long end of the OIS curve- any currency on which interbank swaps are collateralised in USD (so you need to discount on the cross-ccy OIS curve)- AUD, if you put 3M/6M swaps in both the 3M and 6M curve- EUR, if you put EONIA/3M swaps in the EONIA curve similarly to the USD case (and if you put 3M/6M swaps in the 3M curve, you ahve a 3-curve system).

kypr · July 10th, 2012, 10:10 pm

Hi mathmarc,Yes, agreed.Hi jschnaz,Yes agreed with these cases + maybe NOK (similar to AUD).