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With the transition from LIBOR to SOFR, will the LIBOR Market Model be replaced by a new model? Perhaps this has already happened. If yes, what is this new model? If not, will the LIBOR Market Model "live on" after the transition to SOFR?

Thanks!

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    $\begingroup$ This paper explains that LMM will live on and be perfectly fine for the new RFR rates also. Ps: the authors of the paper were nominated for "quant of the year" award for that paper, it's a really good paper to read. $\endgroup$
    – Jan Stuller
    Commented Jan 17, 2022 at 16:10
  • $\begingroup$ @JanStuller In this paper backward-looking forward rates (term rates deducted from SOFR) are modelled as well as forward-looking forward rates (defining in the OIS swap rates, to quote the authors), right ? $\endgroup$
    – Olórin
    Commented Sep 10, 2023 at 17:15
  • $\begingroup$ @Olórin: correct. $\endgroup$
    – Jan Stuller
    Commented Sep 11, 2023 at 9:29
  • $\begingroup$ @JanStuller So this model can diffuse at the same time backward-looking forward rates of a given tenor T and forward-looking forward rates defined in the OIS swap rate manner. But what about if for instance I need a model diffusing at the same time ESTR 3M (backward-looking) forward rates and EURIBOR 3M (forward-looking) forward rates ? The $r_t$ from the paper cannot be used to model both, right ? Unless the EURIBOR3M could be defined as in the old single-curve manner, using only the RFR ESTR, which it obviously cannot, as far as I know. $\endgroup$
    – Olórin
    Commented Sep 12, 2023 at 6:46

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