A mean-field extension of the LIBOR market model

Sascha Desmettre, Simon Hochgerner, Sanela Omerovic, Stefan Thonhauser

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number2250005
Number of pages35
JournalInternational journal of theoretical and applied finance
Volume25
Issue number1
DOIs
Publication statusPublished - 1 Feb 2022

Keywords

  • Black's formula
  • Exploding rates
  • LIBOR market models
  • Life insurance portfolios
  • Mean-field games
  • Solvency II
  • Valuation of long-Term guarantees

ASJC Scopus subject areas

  • Economics, Econometrics and Finance(all)
  • Finance

Fields of Expertise

  • Information, Communication & Computing

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