say the floating leg of the vanilla interest rate swap pays quarterly. Is the pay index the 3 month libor or the forward rate implied from the accrual period? Without the holiday adjustment, the libor and forward rate are of the same tenor. However, the tenor of the forward rate implied from the accrual period is not necessary 3 months when there is holiday adjustment.What is the floating rate convention for vanilla ir swaps? libor or forward rate?

Your question is ill-formed. The answer to it, strictly speaking, is that it's both. Moreover, they have to be consistent, holiday adjustment or not (except VERY few special cases).Specifically, let's say the floating fixing is tomorrow, the 3rd of March. The index that will be used for the subsequent payment will be the 3M LIBOR as published by the BBA tomorrow. However, this value is not known, but what is known is the 3M LIBOR fwd rate starting the 3rd of March. That fwd rate should have the same exact settlement details as the rate that will be released as the fixing tomorrow.

Agreed the question could perhaps be phrased better. The dates in a swap are typically generated from either the start date (most common) or the end date and are subject to date rolls. For example, the payment dates for a quarterly spot-starting floating swap leg would be 3 months from today, 6 months from today, 9 months from today and so on. So, they are defined by the terms of the particular swap in question. The dates for a floating rate index are always generated by its own convention relative to future spot dates. So a string of quarterly floating index rate periods would be generated thusly: the first end date is 3 months from spot, the second end date is 3 months from the 1st payment date, the 3rd is months from the second payment date and so on. Hopefully Is my language clear enough to see that there is a slight difference in the way the dates are calculated. It is not unusual for the two to go slightly out of synch even when the periodicity (e.g. quarterly) is supposed to be the same. So sometimes a swap floating leg may have a 90 day period then the comparable floating rate has 91 days. As Martinghoul has noted both conventions have to be carefully observed when forecasting floating side cash flows. You need to forecast the floating rate according to the particulars of its own convention and then you have to apply it to your swap floating legs as they are defined.

Alternately, you can assume the problem away by assuming that the swap floating leg periods are always the same as the reference floating rate periods (even when they actually are not). This assumption means you are actually using a simplification called the Floating Rate Note (FRN) method to value the floating leg. Many people do this. Most of the time it works just fine.

Sorry if my question is not clear. Let me be more specify. Suppose you have a 1 year "vanilla" interest rate swap with quarter floating rate payment. i.e., the floating rate index is a 3 months libor. However, I have seen two ways of computing the forward libor. I was not sure which one is correct.Say the 1 year floating leg start on on Feb 17 2009 and end on Feb 17 2010. The accrual periods, only adjusted to weekends, areFeb 17 2009, May 18 2009May 18 2009, Aug 17 2009Aug 17 2009, Nov 17 2009Nov 17 2009, Feb 17 2010Note that the May 17 2009 is Sunday, so it is adjusted to May 18 2009.There are two ways to compute the forward rate for period May 18 to Aug 17 2009.(1) ForwardRate(May 18 2009, Aug 17 2009), which is "naturally" the same as the accrual period.(2) ForwardRate(May 18 2009, May 18 2009 + 3 months), which is using the 3 months libor definition.Note that the dates I am using is the effective dates (not the observation). Because of the holiday adjustment, (1) and (2) are slightly different.As far as the "vanilla" IR Swap, is the floating rate payment using (1) or (2)?

QuoteOriginally posted by: danielyngSorry if my question is not clear. Let me be more specify. Suppose you have a 1 year "vanilla" interest rate swap with quarter floating rate payment. i.e., the floating rate index is a 3 months libor. However, I have seen two ways of computing the forward libor. I was not sure which one is correct.Say the 1 year floating leg start on on Feb 17 2009 and end on Feb 17 2010. The accrual periods, only adjusted to weekends, areFeb 17 2009, May 18 2009May 18 2009, Aug 17 2009Aug 17 2009, Nov 17 2009Nov 17 2009, Feb 17 2010Note that the May 17 2009 is Sunday, so it is adjusted to May 18 2009.There are two ways to compute the forward rate for period May 18 to Aug 17 2009.(1) ForwardRate(May 18 2009, Aug 17 2009), which is "naturally" the same as the accrual period.(2) ForwardRate(May 18 2009, May 18 2009 + 3 months), which is using the 3 months libor definition.Note that the dates I am using is the effective dates (not the observation). Because of the holiday adjustment, (1) and (2) are slightly different.As far as the "vanilla" IR Swap, is the floating rate payment using (1) or (2)?I understand now. The answer to your question is, IMHO, either/both/whatever. I have run into a similar issue with Eurodollar contracts, where the forward rate period on the contract (defined as IMM date to IMM date) is actually different from the period on the LIBOR index used to compute the settlement px for the contract when it matures (3M from date to date). So I thought I'd go and check with the ultimate authority, specifically, Burghardt's 'Eurodollar Futures and Options Handbook'. Here's what the Man says and I quote: 'As date mismatches go, the differences are small, and you would not be far wrong if you used the [futures-implied fair] rate as the fair value of the forward 3-month LIBOR to which the futures contract settled.' Thus, it's a matter of practicality to use the forward you describe in (1) (it's easy to get that fwd out of your curve) as a value for the expected fixing in (2). Does that help/answer your question?

Hello Martinghoul,Thank you very much for spending time answer my question. I agree that it depends on practicality. Is it fair to say it depends on which convention is used for bootstrapinng the interest rate curve? In other words, pricing and curve bootstrapping must use the same convention so that the reference swaps can be priced to par.

"... pricing and curve bootstrapping must use the same convention so that the reference swaps can be priced to par." Bingo, you've just stated the answer. Indeed, pricing an input par swap when you taken pains to forecast all the floating side rates and then finding it doesn't exactly value to par is how most people stumble into this issue. It turns out that if you build the zero curve the way most people do you are doing it in a way that implicitly assumes that the floating sides of the par input swaps are valued using the FRN approximation method noted below. Usually this works 100% because there are usually no floating period mismatches. Sometimes there are, though. If you want to value floating swap legs forecasting the precise floating rate index settings you'll have to do something more clever when building your curve, that is, if you want each and every par input swap to price to par 100% of the time.

except length of accrual tenor mismatchs, I think start date also mismatchs if fixing days dont coincide with settle days of libor rates. Taking the period "May 18 2009 to Aug 17 2009" for example, assume fixing days is 5 (bds) and settle days is 2 (bds), then fixing date is May 11 2009 and 3m libor start at May 13 2009 and end at Aug 13 2009...but accrual period is "May 18 2009 to Aug 17 2009".