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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 language | English |
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Article number | 2250005 |
Number of pages | 35 |
Journal | International journal of theoretical and applied finance |
Volume | 25 |
Issue number | 1 |
DOIs | |
Publication status | Published - 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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FWF - Risk Modelling - Analysis, Simulation and Optimization
Thonhauser, S. M. & Pojer, S.
1/07/20 → 30/06/24
Project: Research project