Bootstrapping SOFR Curves with Swap Payment Lags
Summary
The document considers how a payment delay affects discount-factor bootstrapping for SOFR swaps. It distinguishes the accrual period, which determines the interest amount, from the later cash-flow payment date. The answer argues that the payment lag’s convexity adjustment is generally very small, so it can usually be ignored when bootstrapping the curve. For a single-period swap at its mid-market rate, the net payment is zero; shifting the date of that zero payment contributes only a small convexity effect.
For a longer swap with multiple payments, the curve already contains discount factors for earlier dates, while the final maturity discount factor is the new value being solved for. Applying the payment lag to the final cash flow can slightly change the valuation, but the answer characterizes the impact as tiny and increasingly discounted for longer maturities. This is a practical approximation, not a complete derivation of a lag-adjusted curve. It does not specify conventions or provide a general formula for cases where the adjustment is material.
Key ideas
- The accrual period and the cash-flow payment date are separate dates in a swap with payment lag.
- Payment lags introduce a convexity adjustment that is generally treated as negligible in the described bootstrapping context.
- A mid-market single-period swap has a net payment of zero, so its payment delay affects value only through convexity.
- For a longer swap, the final payment date can slightly affect the maturity discount factor being bootstrapped.
- The approximation is context dependent and does not provide a formula for material lag effects.
Tags
Full text
# Bootstrapping SOFR curve and Swap Payment Lag # Bootstrapping SOFR curve and Swap Payment Lag Can someone provide me an intuitive explanation of how discount factors are bootstrapped for SOFR when Swaps are trading with payment delay/ lag (e.g. of 2 business days). I can intuitively derive the discount factors when the payment lag is zero e.g. | Trade Date | Value Date | Tenor | Maturity | Swap Rate | Pay Lag | | 1 Feb 2023 | 3 Feb 2023 (T+2) | 1M | 3 Mar 2023 | 3.5% | 0 | Since Payment Lag = 0, the cash flow date is 3 Mar 2023. Now the discount factor from 3-Feb-2023 to 3-Mar-2023 equals 1/(1+3.5%*28/360) ==> 0.99728516 This would then get multiplied with the discount factor for 3 Feb 2023 to arrive at the final discount factor from 1-Feb-2023 to 3-Mar-2023. However, when the payment lag is 2 days, then the Cash Flow Date is 7 Mar 2023, although accrual period remains the same (3 Feb 2023 to 3 Mar 2023). How would the discount factors get calculated, in this scenario ? Appreciate any clarity from your side. I hope the question is clear. ## Answer by river_rat (score 1) https://quant.stackexchange.com/a/74768 The convexity adjustments for payment lags are usually so tiny (see Why is there a convexity adjustment if the payment date differs from Libor end date?) that we can ignore them for the bootstrapping. So you only need to worry about the accrual periods etc ## Answer by Attack68 (score 1) https://quant.stackexchange.com/a/81199 The point that @river_rat is making can also be expanded. Single period swaps only have one payment and for mid-market rates that payment is netted to zero. E.g. a 5m SOFR swap on an Annual-Annual basis has one payment in 5months. For a mid-market swap (which are used to bootstrap the curve) the net payment will be zero, meaning the payment lag for a net payment of zero is a pure convexity adjustment only, and it is also very short dated (only 5 months) to maturity so it can be effectively ignored. For longer swaps e.g. 10Y, you will have 10 payments. The 10Y swap will only bootstrap the 10y DF so all other discount factors are available to calculate with a 2day payment lag up to that point. This may make small differences, but again we are only talking hundredths of a basis point. For this swap you will only mis-value the last payment by two days, and the longer the swaps get the more those differences will be discounted anyway, so it is also going to get less impactful.
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.