A mean-field extension of the LIBOR market model

Sascha Desmettre, Simon Hochgerner, Sanela Omerovic*, Stefan Thonhauser

*Korrespondierende/r Autor/-in für diese Arbeit

Publikation: Beitrag in einer FachzeitschriftArtikelBegutachtung

Abstract

In this paper, 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 Black's 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.

Originalspracheenglisch
Aufsatznummer2250005
Seitenumfang35
FachzeitschriftInternational journal of theoretical and applied finance
Jahrgang25
Ausgabenummer1
DOIs
PublikationsstatusVeröffentlicht - 1 Feb. 2022

ASJC Scopus subject areas

  • Volkswirtschaftslehre, Ökonometrie und Finanzen (insg.)
  • Finanzwesen

Fields of Expertise

  • Information, Communication & Computing

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