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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.

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1 Answer 1

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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

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  • $\begingroup$ Thanks river_rat, will ponder upon this. Got a link to another thread ..quant.stackexchange.com/questions/64342/… appears relevant to my question. $\endgroup$ Commented Feb 28, 2023 at 8:14
  • $\begingroup$ Convexity adjustments are small/negligible for a non-delayed versus a delayed payment swap, that is true. But this does not mean that swaps with different payment lags have the same mid-market price. It is important to correctly account for the real timing of cashflows. $\endgroup$
    – Attack68
    Commented Mar 23 at 16:17
  • $\begingroup$ True but for typical curves and a typical payment delay of 2 days we are talking a difference in mids of 0.17bps at the 10yr point? $\endgroup$
    – river_rat
    Commented Mar 25 at 14:59

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