PDEs for pricing interest rate derivatives under the new generalized Forward Market Model (FMM)

TL;DR

This paper introduces PDEs for pricing interest rate derivatives under the new generalized Forward Market Model, providing a novel PDE approach for RFR derivatives and comparing it with Monte Carlo methods.

Contribution

It derives the first PDE formulations for RFR derivatives under the generalized FMM and adapts finite difference methods for their numerical solution.

Findings

PDE methods effectively price RFR derivatives.

Finite difference adaptations handle spatial mixed derivatives.

PDE and Monte Carlo results are compared for validation.

Abstract

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.