A mean-field extension of the LIBOR market model

Sascha Desmettre, Simon Hochgerner, Sanela Omerovic and Stefan Thonhauser

Papers from arXiv.org

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.

Date: 2021-09
New Economics Papers: this item is included in nep-isf
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Published in International Journal of Theoretical and Applied Finance Vol. 25, No. 01, 2250005 (2022)

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2109.10779

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