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