  In this paper, we present an alternative perspective on the mean-field LIBOR
market model introduced by Desmettre et al. in arXiv:2109.10779. Our novel
approach embeds the mean-field model in a classical setup, but retains the
crucial feature of controlling the term rate's variances over large time
horizons. This maintains the market model's practicability, since calibrations
and simulations can be carried out efficiently without nested simulations. In
addition, we show that our framework can be directly applied to model term
rates derived from SOFR, ESTR or other nearly risk-free overnight short-term
rates -- a crucial feature since many IBOR rates are gradually being replaced.
These results are complemented by a calibration study and some theoretical
arguments which allow to estimate the probability of unrealistically high rates
in the presented market models.
