Framing a SOFR-to-LIBOR Forward Rate Conversion

Summary

The document asks how to translate a 90-day SOFR market rate into a comparable three-month LIBOR rate. It highlights a key timing distinction: SOFR for the accrual period is compounded in arrears, so the realized period rate is not known until the period ends, whereas the question seeks an equivalent forward-looking LIBOR rate.

The author proposes using a generalized forward market model and points to a drift relationship in a cited paper as a possible way to consolidate the rates. They ask whether the practical route is to determine a SOFR forward and then infer the LIBOR forward using no-arbitrage reasoning. However, the document contains no answer, derivation, calibration details, or worked conversion. It therefore identifies the modeling issue and a candidate framework but does not establish that the suggested equation applies or provide a usable conversion procedure. Any implementation would need precise rate conventions, dates, curves, and model assumptions.

Key ideas

• The question concerns conversion between a 90-day SOFR market rate and a three-month LIBOR rate.
• SOFR accrues in arrears, leaving the realized period rate unknown until accrual ends.
• The author considers a generalized forward market model and a drift relation for combining the rates.
• No-arbitrage reasoning is proposed as a possible bridge from a SOFR forward to a LIBOR forward.
• The document supplies no derivation or validated conversion formula, so its proposal remains unresolved.

Tags

# 90 day SOFR market rate to equivalent 3M Libor rate conversion


# 90 day SOFR market rate to equivalent 3M Libor rate conversion












I am trying to convert a 90 day SOFR market rate into a fair equivalent 3 month Libor rate. I understand since SOFR is by nature an in-arrears backwards looking rate, so for SOFR instruments such as a 90 day SOFR swap we need to wait until the end of the accrual period to know the fixing value.

I'm trying to use the Generalized Forward market model from this paper. Section 2.5 mentions how the two rates can be consolidated. I believe the equation that does so is equation 20 on page 9 :Drift(Rj ; Q)(t) − Drift(Rj ; Q d )(t) = τη(t)ση(t)(t)gη(t)(t) 1 + τη(t)Rη(t)(t) σj (t)gj (t)ρη(t),j

Is the key to converting between a 90 day SOFR market rate and a 3 month Libor date in determining the SOFR forward, and then confirming this as the Libor forward by the principal of no arbitrage? If I am completely wrong, would anyone be able to suggest a better conversion formula or methodology? Thank you for your guidance

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