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

López-Salas, José Germán; Pérez-Rodríguez, Soledad; Vázquez, Carlos

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http://hdl.handle.net/2183/38166

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

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LopezSalas_JoseGerman_2024_PDEs_for_pricing_interest_rates_derivatives.pdf (623.76 KB)

Identifiers

URI: http://hdl.handle.net/2183/38166

DOI: 10.1016/j.camwa.2024.06.010

Publication date

2024-09-01

Authors

López-Salas, José Germán

Pérez-Rodríguez, Soledad

Vázquez, Carlos

Bibliographic citation

J. G. López-Salas, S. Pérez-Rodríguez, y C. Vázquez, «PDEs for pricing interest rate derivatives under the new generalized Forward Market Model (FMM)», Computers & Mathematics with Applications, vol. 169, pp. 88-98, sep. 2024, doi: 10.1016/j.camwa.2024.06.010.

Abstract

[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 [1] 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 [2] 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.