# Are forward rates for an IRS computed between reset dates or between start dates?

In order to price the floating leg of an IRS I am computing forward rates for future coupons, but I'm not sure whether I have to compute such rates between reset dates or between start dates.

My intuition tells me that forward rates should be calculated between reset dates because that's when you fix the rate for each coupon, but I've seen that in practice many people calculates them between start dates and it confuses me a little bit, because my logic says that in such scenario you'd be estimating a rate that is already known.

I hope you guys can help me. Thanks!

For each payment of the floating leg on a swap, you have:

Where the fixing date is normally 2 business days before the accrual start and the payment date will normally coincide with the accrual end period. I am presenting a general case since this will depend on the conventions for the particular currency.

For example, in EUROS the convention for Euribor is 2 business day lag for the fixings and modified following adjusted for the payment date. For LIBORS, we'll see where the LIBOR transition takes us.

Regarding the forward rate estimation, you want to estimate the rate that would start on the Accrual Start Date and end on the Accrual End Date.

Notice that when you get the fixing for a Euribor, it refers to the period that would start in 2 business days. If you trade a vanilla swap, you will already know the first floating rate. The same happens with caps and floors, there is no optionallity in the first optionlet because the fixing is already known.

• Hi David! As you well point, when you trade a vanilla swap you already know the first floating rate (due to -2D fixing lag). In that case, you don't estimate a forward rate for your first coupon, even when it starts accruing in two days. So why not following the same logic for the next coupons? I.e. estimating forward rates from FixingDate(i) to my FixingDate(i+1) and accruing with such rate from StartDate(i) to EndDate(i)... What am I missing? Thanks for your help! Mar 2, 2020 at 16:29
• You have to separate two different things: (1) the date of the information you have and (2) the dates of what you want to determine. Today, you are estimating forwards using today's market prices (deposits, swaps, fras, futures, etc) and each forward you estimate will have it's own dates. If you pass the fixing date, it's no longer an estimate because you already know the true value. One or more days before the fixing it's a forward but on the fixing day (after 10am) or any day after that, it's a fixed rate. Mar 2, 2020 at 17:05
• Okay, so you stop calculating forward rates for each coupon once its respective fixing date is reached and as of that date you calculate your next payment with the rate you just fixed? In that case, in the dates between fixing and start you would have 2 fixed rates "alive" at the same time: The one for the current coupon and the one for the coupon that is about to start... Am I right? Thanks again! Mar 2, 2020 at 17:42
• No, that is not correct. You determine the future forward with your yield curve and not with past fixings. The yield curve is a representation of spot rates or discount factors per tenor, and is extracted from market prices of instruments with different maturities. You estimate forwards based on that curve because in theory you could replicate them with spot trades. A fixings is simply a rate that was determined in the past for the interest accrual of a specific period. Mar 2, 2020 at 17:53
• @DavidDuarte there are times when the accrual dates do not align with the underlying valuation dates for the specific rate, as a case in point, the regularly traded IMM swaps which accrue only between IMM dates but 3M libor does not necessarily accrue between IMM dates. As a result date schedulers for IRS usually split accrual dates from rate valuation dates if they are detailed enough.
– Attack68
Mar 2, 2020 at 18:12

For IRS schedules there are the following different sets of dates:

Payment dates: the dates on which cashflows are exchanged.
Accrual dates: these dates define how much interest is accrued (given a specific rate either fixed or floating)
Reset/Fixing dates: this is the date a floating rate publication is actually calculated and made public, i.e. displayed on a screen.
Rate Valuation Dates: these are the dates that the published floating rate typically address, e.g. in USD LIBOR is published two days in advance, so a 3M rate in USD published on 1st Feb 2020, would have a start date of 3rd Feb to 3rd May (adjusting for weekends/holidays under the normal convention). Using a discount factor curve you would usually derive the rate published on 1st Feb via the discount factors on 3rd Feb and 3rd May.

Hope that helps.

• Let's suppose I am pricing a vanilla IRS that has already started. The current coupon pays on Feb 3rd so the next coupon goes from Feb 3rd to May 3rd and my fixing date is Jan 30 (due to the weekeend). If I am pricing this swap on Jan 29, should I estimate forwards until Jan 30 or until Feb 3rd? Thanks! Mar 2, 2020 at 16:42
• You need to estimate the forward that is applicable between the value start dates of feb 3 and may 3, however, you will only need to estimate this forward until around 11am on jan 30, since after the publication you have the known value which you must insert into the floating leg for correct valuation.
– Attack68
Mar 2, 2020 at 18:07

The forward rate is estimated at the Libor valuation date = reset date + the reset gap (namely 1, 2 or 3 days) (not the accrual start date). In the case of standard vanilla swaps, the accrual start date is equal to the reset date + the reset gap: this I believe is the case that Davide Duarte talks about. However, for the general case, the accrual date could be different from the valuation date. Therefore, the general answer would be that :

The forward rate is calculated at the reset date + the reset gap (1, 2 or 3 days depending on the currency) which could coincide with the accrual start date in case of standard vanilla swaps