I am a bit confused on what is going on regarding the new benchmark rate SOFR. My understanding is that SOFR is to replace Libor. However, I also get information on Fed fund OIS discounting is replaced by SOFR discounting .
The market is using SOFR discounting for all sorts of quotations already (not FF). For example, swaption vol is quoted with SOFR discounting, CME and LCH moved to SOFR PAI and discounting on Oct. 16 2020 on new AND legacy swaps.
For EUR cleared, major CCPs did this since July 27 2020.
The market switched to discounting with the relevant RFR rates on the dates above. Hence, if you have a dual stripped curve (e.g. 3m US libor), you use SOFR and no longer OIS (FF).
ISDA fallbacks will apply from 31 December 2021 for GBP, JPY, CHF and Euro-LIBOR and from 30 June 2023 for USD LIBOR. Note that the FED have issued supervisory guidance encouraging banks to “cease entering into new contracts that use USD LIBOR as a reference rate as soon as practicable and in any event by December 31, 2021”.
That said, it does NOT get rid of FF. It will co-exist, with SOFR being the more widely used (and being the choice for discounting).