I hope to find somebody here to shed some light onto this topic.
I remember from my studies that in order to properly deal with the Libor rates with fixing in arrears one has to go through some convexity adjustment, taking the volatility of the forward rate into account, as the in-arrears fixing suggests using some unnatural numeraire than the Libor native numeraire. The convexity adjustment comes with the change of numeraire.
When it comes to RFR, especially to backward-looking in-arrears forward rate, nobody cares in the current literature about this kind of convexity adjustment.
To me, apart from some days lag or shift, the RFR behaves almost the same as the Libor-in-arrears rate which remains uncertain till fixing date = payment date.
In chapter 2.3 of paper "Looking Forward to Backward-Looking Rates... " Lyashenko/Mercurio state that the forward looking rate and the backward-looking rate match if the relevant period they are related with is in the future. I am missing the logic of the numeraire mismatch in this context. I am sure the guys are right, I am missing the point.
Where am I wrong? Is that wrong comparing the backward-looking in-arrears RFR with Libor-in-arrears before entering into the period they are valid to?