Which Dates Define Forward Rates for Swap Floating Coupons
Summary
The document explains how forward rates relate to the dates in an interest rate swap's floating leg. It distinguishes payment dates, accrual dates, reset or fixing dates, and rate valuation dates. The rate being estimated is associated with the period over which interest accrues, from the accrual start to the accrual end. Since a published fixing can refer to a period that begins after the fixing date, those dates should not be conflated.
For a standard vanilla swap, the rate valuation date—typically the reset date plus a currency-specific lag—often coincides with the accrual start date. In that common case, deriving the forward from discount factors at the accrual boundaries is consistent with the coupon period. The document notes that conventions vary by currency and that the general case can have distinct valuation and accrual dates. It also observes that the first floating coupon may already be fixed at trade time, so it is known rather than forecast. The exchange gives convention examples but does not set out a complete pricing formula or cover every market convention.
Key ideas
- Swap schedules distinguish payment, accrual, fixing, and rate valuation dates.
- The forward rate corresponds to the rate period from accrual start through accrual end.
- A fixing date may precede the period to which the published rate applies.
- In standard vanilla swaps, the rate valuation date often matches the accrual start, subject to currency conventions.
- The first floating coupon can already be fixed when a swap is traded.
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Full text
# Are forward rates for an IRS computed between reset dates or between start dates? # 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! ## Answer by David Duarte (score -1, accepted) https://quant.stackexchange.com/a/51446 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. ## Answer by Attack68 (score 2) https://quant.stackexchange.com/a/51443 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. ## Answer by Xman (score 0) https://quant.stackexchange.com/a/51459 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
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