Constructing a SOFR Discount Curve from Term Rates and Swaps
Summary
The discussion outlines a practical way to build a SOFR discount curve using term SOFR fixings for shorter maturities and fixed-versus-SOFR swaps for the longer end. It describes the swap legs as annual fixed payments on an Actual/360 basis and overnight SOFR compounded in arrears. For the short end, term fixings can be treated as single-payment instruments, while monthly and quarterly SOFR futures offer an alternative source of similar curve inputs.
The answer notes that three- and six-month term SOFR can be used in one curve because both reference compounded overnight rates. It also cautions that a front-month futures contract reflects realized daily SOFR settings as its settlement period unfolds, creating dependence on historical fixings. The advice is a brief practitioner response rather than a full bootstrap recipe: it does not give equations, market conventions in detail, or an empirical comparison of instrument choices, and its recommendations reflect the market context described in the document.
Key ideas
- Use fixed-versus-SOFR swaps to anchor the longer maturities of the discount curve.
- Term SOFR fixings can provide short-end inputs and may be modeled as single-payment instruments.
- SOFR futures are an alternative short-end source because term fixings are derived partly from futures markets.
- Three- and six-month term SOFR can coexist in one curve because both are based on compounded overnight rates.
- Front futures contracts require attention to daily realized SOFR settings during their settlement month.
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# SOFR Discount Curve Construction in Nov 2021 # SOFR Discount Curve Construction in Nov 2021 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? ## Answer by dm63 (score 11, accepted) https://quant.stackexchange.com/a/68820 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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