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The Mean Field Market Model Revisited

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  • Manuel Hasenbichler
  • Wolfgang Muller
  • Stefan Thonhauser

Abstract

In this paper, we present an alternative perspective on the mean-field LIBOR market model introduced by Desmettre et al. in arXiv:2109.10779. Our novel approach embeds the mean-field model in a classical setup, but retains the crucial feature of controlling the term rate's variances over large time horizons. This maintains the market model's practicability, since calibrations and simulations can be carried out efficiently without nested simulations. In addition, we show that our framework can be directly applied to model term rates derived from SOFR, ESTR or other nearly risk-free overnight short-term rates -- a crucial feature since many IBOR rates are gradually being replaced. These results are complemented by a calibration study and some theoretical arguments which allow to estimate the probability of unrealistically high rates in the presented market models.

Suggested Citation

  • Manuel Hasenbichler & Wolfgang Muller & Stefan Thonhauser, 2023. "The Mean Field Market Model Revisited," Papers 2402.10215, arXiv.org.
    • Handle: RePEc:arx:papers:2402.10215
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    References listed on IDEAS

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    1. Simon Hochgerner & Florian Gach, 2018. "Analytical Validation Formulas for Best Estimate Calculation in Traditional Life Insurance," Papers 1802.07009, arXiv.org, revised Jul 2019.
    2. Florian Gach & Simon Hochgerner, 2021. "Estimation of future discretionary benefits in traditional life insurance," Papers 2101.06077, arXiv.org, revised Jul 2022.
    3. Gach, Florian & Hochgerner, Simon, 2022. "Estimation Of Future Discretionary Benefits In Traditional Life Insurance," ASTIN Bulletin, Cambridge University Press, vol. 52(3), pages 835-876, September.
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    1. Florian Gach & Simon Hochgerner & Eva Kienbacher & Gabriel Schachinger, 2023. "Mean-field Libor market model and valuation of long term guarantees," Papers 2310.09022, arXiv.org, revised Nov 2023.
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    3. Sascha Desmettre & Simon Hochgerner & Sanela Omerovic & Stefan Thonhauser, 2021. "A mean-field extension of the LIBOR market model," Papers 2109.10779, arXiv.org.

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