# SOFR - Notice of Payment

I am reading SOFR USER Guide - https://www.newyorkfed.org/medialibrary/Microsites/arrc/files/2019/Users_Guide_to_SOFR.pdf

I am having trouble understanding SOFR payment in arrears, especially lockout and lookback.

Lockout or Suspension Period: Use the averaged SOFR over current interest period with last rates set at the rate fixed k days before the period ends (a 2-5 day lockout has been used in most SOFR FRNs).

Lookback: For every day in the current interest period, use the SOFR rate from k days earlier. (a 3-5 day lookback has been used in SONIA FRNs)

Does anyone has an example or point to source to explain lockout and lookback ?

These are two simple concepts that address a practical problem when settling coupons that are only calculated in-arrears. Let us assume that $$r_i$$ is the SOFR fixing valid for business day $$i$$ (up until next bus day, $$i+1$$). Denote by $$n_i$$ the number of calendar days between $$i$$ and $$i+1$$, divided by the appropriate nbr of days in a year (e.g. 360 or 365).

Assume that you wish to calculate the coupon for the accrual period from $$t$$ to $$T$$, that is also due to be paid at time $$T$$. Now you seek to compound the daily SOFR rates in order to determine the payment amount; but you will realize that the last fixing (the one from $$T-1$$, as the accrual end date is excluded from compounding) will be available to you "too late" (usually at $$T$$, depending on which time zone you sit in & because central banks usually publish these rates with a delay). This is too little time for counterparties to reconcile numbers and settle payments at $$T$$. Hence, you have two (or more) options, to work around this problem:

1. a $$k$$-day lookback (without observation shift): $$\Pi_{i=t}^{T-1} (1 + r_{i-k} n_i) -1$$ In simple words, for compounding the rate of Wednesday, you simply use the SOFR fixing that happened $$k$$ days before this Wednesday. Do note that there is also a variant of this, where you also shift the day-count weights of the fixing, leading to $$\Pi_{i=t}^{T-1} (1 + r_{i-k} n_{i-k}) -1$$. In both ways, you know the final rate now $$k$$ days ahead of payment.

2. a $$k$$-day lockout: $$\Pi_{i=t}^{T-1-k-1} (1 + r_i n_i) \Pi_{i=T-1-k}^{T-1} (1 + r_{i-k} n_i) -1$$ This simply means that you take the rate from $$k$$ days before the accrual end date and use this constant value for the remainder of the period. Also in this case, you know the final rate now $$k$$ days ahead of payment.

Hope this helps.

• Thank you so much for the detailed explanation. Feb 2, 2022 at 20:00
• Please consider accepting one of the posted answers if you think that your question is resolved by it. Feb 3, 2022 at 11:39

KevinT's answer has it all. I am just adding to the section:

"Do note that there is also a variant of this, where you also shift the day-count weights of the fixing, ..."

The DataFrame below illustrates the so called BOS (backward observation shift) Focus on Monday 3rd June: in both approaches you take the rate on May 24th (5 business days prior; or any appropriate day)

Under Lookback
- you apply the rate for Monday 3rd June - 4th June (1 day only)

- the accrual for this day is (((2.37% )/360)*1)+1 = 1.000065833

Under Backward Shift approach
- you apply it for Friday 24th - Tuesday 28th (4 days)

- the accrual for this day is (((2.37% )/360)*4)+1 = 1.000263333

To sum up: on Monday 3rd June
- Lookback will accrue 1.000065833 * Nominal
- BOS will accrue 1.000263333* Nominal
• Thank you so much for the detailed explanation. Feb 2, 2022 at 20:00