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Suppose an adjustable-rate mortgage loan was issued in 2016 and tied to "1yr WSJ LIBOR".

Suppose the loan will start adjusting in 2023.

Assume LIBOR will be phased out quickly after 2021 and de-facto replaced by SOFR, as often reported in the industry press.

Assume that since there are still ~3 years left until conversion, neither the lender nor the borrower have retained an attorney to negotiate the LIBOR to SOFR transition.

My question then is, from a purely mathematical and logical standpoint (let's say you are to be an impartial arbiter in the negotiation between lender and borrower), how do you convert "1yr WSJ LIBOR" to SOFR?

My initial point of confusion is that the former is a one-year term rate, while the latter is an overnight rate, so they seem fundamentally incovertible without some sort of arbitrary fudge factor. What am I missing?

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