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A mean-field extension of the LIBOR market model

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  • Sascha Desmettre
  • Simon Hochgerner
  • Sanela Omerovic
  • Stefan Thonhauser

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.

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  • Sascha Desmettre & Simon Hochgerner & Sanela Omerovic & Stefan Thonhauser, 2021. "A mean-field extension of the LIBOR market model," Papers 2109.10779, arXiv.org.
    • Handle: RePEc:arx:papers:2109.10779
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    1. Nicole El Karoui & Stéphane Loisel & Jean-Luc Prigent & Julien Vedani, 2017. "Market inconsistencies of the market-consistent European life insurance economic valuations: pitfalls and practical solutions," Post-Print hal-01242023, HAL.
    2. Simon Hochgerner & Florian Gach, 2018. "Analytical Validation Formulas for Best Estimate Calculation in Traditional Life Insurance," Papers 1802.07009, arXiv.org, revised Jul 2019.
    3. Mark Joshi & Riccardo Rebonato, 2003. "A displaced-diffusion stochastic volatility LIBOR market model: motivation, definition and implementation," Quantitative Finance, Taylor & Francis Journals, vol. 3(6), pages 458-469.
    4. Gerhold, Stefan, 2011. "Moment explosion in the LIBOR market model," Statistics & Probability Letters, Elsevier, vol. 81(5), pages 560-562, May.
    5. Marek Rutkowski & Marek Musiela, 1997. "Continuous-time term structure models: Forward measure approach (*)," Finance and Stochastics, Springer, vol. 1(4), pages 261-291.
    6. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
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