On July 29, 2021, the Alternative Reference Rates Committee (ARRC) formally recommended the forward-looking term rates based on SOFR published by the CME Group.
CME currently publishes Term SOFR for 1M, 3M, 6M, and 12M (Bloomberg tickers SR1M, SR3M, SR6M, SR1Y and Refinitiv tickers .SR1M, .SR3M, .SR6M, .SR1Y [although for some reason I see the data in Bloomberg but do not have access in Refinitiv]). The advantage of Term SOFR is it is "forward looking", so my understanding is you can get rid of all the nasty "in arrears" calculations since Term SOFR is a forward looking rate.
It seems it makes sense to use Term SOFR to construct the short end of a SOFR discount curve. As for the long end, I have a suspicion that CME's OIS swaps would fit this purpose (specifically I am referring to SOFR floating vs. Fixed swap rates and not some basis swap such as SOFR vs. Effective Fed Funds Rate or SOFR vs. Libor). Although, it is unclear to me why one wouldn't just use OIS swaps for the entire discount curve. My understanding is that Term SOFR is constructed partially from the OIS swaps anyway.
In addition, I am having trouble discovering the mechanics behind the Term SOFR and OIS rates. I assume Term SOFR are bullets and the OIS has some kind of annual coupon payment both with Actual/360 day count conventions.
Given the somewhat recent announcement from ARRC, can anyone provide me an example on recommended practice in constructing a discount curve from these CME tools?