The mean field market model revisited

In this paper, we present an alternative perspective on the mean-field LIBOR market model introduced by Desmettre et al. (Int J Theor Appl Finance, 2022. https://doi.org/10.1142/S0219024922500054). 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 in-arrear 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.