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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?

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    $\begingroup$ Great question. I would construct the whole curve based on OIS SOFR Swaps: i.e. Fixed vs. SOFR (where the SOFR floating leg is compounded in arrears). For the short end, say 3 months, if there isn't a bullet SOFR OIS swap, then there should be an "off-the-run" SOFR OIS Swap, i.e. one that started trading (say) 9 months ago as a 1-year OIS SOFR swap and now has 3 months left. I don't think the term SOFR rates you mention are established enough to be used for curve construction yet, and I don't know what instruments they are based on. $\endgroup$
    – Jan Stuller
    Commented Nov 17, 2021 at 19:06
  • $\begingroup$ Disclaimer: I don't trade the USD rates market, so I don't have an in-depth knowledge on the exact mechanics of the OIS SOFR swaps or the Term SOFR rates: the above are just my thoughts based on my intuition and my "non-practitioner" knowledge of the market. $\endgroup$
    – Jan Stuller
    Commented Nov 17, 2021 at 19:09

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Fixed vs SOFR swaps for longer maturities are very liquid, since the interbank market trades these directly now, and these are the best instruments to construct the long end of the curve (2yr to 50yr). The day count is fixed annual Act/360 versus SOFR compounded and paid in arrears.

For the short end, you could use the term SOFR fixings - these should be interpreted as fixed act/360 versus SOFR compounded in arrears with a single payment on each leg. These term SOFR fixings are calculated using an interpolation scheme based on SOFR futures markets. So you could use the futures markets directly and you should get very similar results. There are two series, monthly and quarterly futures, and they have increasing liquidity.

Couple of technical points : for sofr , you are allowed to use the 3m term SOFR and the 6m term SOFR in the same curve. (Whereas , for libor , you cannot do this due to the presence of the basis swap). This is because both rates are based on compounding overnight rates. Secondly , be careful when using the front futures contract. It expires ‘gradually’- meaning, as you go through the settlement month, the overnight rates are being set and compounded using daily settings of SOFR. So there is some historical data dependency.

Good luck , hope this helps.

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    $\begingroup$ Neat answer, thank you, useful for me also. +1 $\endgroup$
    – Jan Stuller
    Commented Nov 18, 2021 at 13:46
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    $\begingroup$ Are you confusing Term SOFR with SOFR Futures? I see daily Term SOFR rates posted in Bloomberg. What is the coupon frequency for Term SOFR and OIS? When you say "paid in arrears", does some special work need to be done to perform the bootstrap? $\endgroup$
    – JoeBass
    Commented Nov 18, 2021 at 17:26
  • $\begingroup$ No I explained term SOFR and futures separately didn’t I? You questions seem already to be answered. Pls clarify. $\endgroup$
    – dm63
    Commented Nov 19, 2021 at 8:54
  • $\begingroup$ Is there any reason that it is not allowed to use 3m term LIBOR and 6m term LIBOR in the same curve? I don't understand why existence of basis swap hinder that behavior. $\endgroup$
    – user13232877
    Commented Nov 30, 2022 at 8:30
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    $\begingroup$ Let’s say there is a 6m basis swap that exists such that 6mLibor can be swapped for 3mLibor +5bp . Then bootstrapping 3m Libor will give you a level for 6m Libor that is 5bp too low. $\endgroup$
    – dm63
    Commented Nov 30, 2022 at 13:07

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