A mean-field extension of the LIBOR market model

TL;DR

This paper extends the LIBOR market model using mean-field theory to improve stability and reduce explosion risk, while maintaining key features like calibration and martingale properties.

Contribution

It introduces a novel mean-field LIBOR market model that preserves essential features and enhances stability, with theoretical proofs and practical numerical methods.

Findings

Proves existence and uniqueness of the MF-LMM.

Develops a Monte Carlo simulation based on interacting particle systems.

Provides numerical analysis demonstrating the model's practical viability.

Abstract

We introduce a mean-field extension of the LIBOR market model (LMM) which preserves the basic features of the original model. Among others, these features are the martingale property, a directly implementable calibration and an economically reasonable parametrization of the classical LMM. At the same time, the mean-field LIBOR market model (MF-LMM) is designed to reduce the probability of exploding scenarios, arising in particular in the market-consistent valuation of long-term guarantees. To this end, we prove existence and uniqueness of the corresponding MF-LMM and investigate its practical aspects, including a Black '76-type formula. Moreover, we present an extensive numerical analysis of the MF-LMM. The corresponding Monte Carlo method is based on a suitable interacting particle system which approximates the underlying mean-field equation.