  In this article we derive partial differential equations (PDEs) for pricing
interest rate derivatives under the generalized Forward Market Model (FMM)
recently presented by A. Lyashenko and F. Mercurio in
\cite{lyashenkoMercurio:Mar2019} to model the dynamics of the Risk Free Rates
(RFRs) that are replacing the traditional IBOR rates in the financial industry.
Moreover, for the numerical solution of the proposed PDEs formulation, we
develop some adaptations of the finite differences methods developed in
\cite{LopezPerezVazquez:sisc} that are very suitable to treat the presence of
spatial mixed derivatives. This work is the first article in the literature
where PDE methods are used to value RFR derivatives. Additionally, Monte
Carlo-based methods will be designed and the results are compared with those
obtained by the numerical solution of PDEs.
