A mean-field extension of the LIBOR market model
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.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2021
- DOI:
- 10.48550/arXiv.2109.10779
- arXiv:
- arXiv:2109.10779
- Bibcode:
- 2021arXiv210910779D
- Keywords:
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- Mathematics - Probability;
- Quantitative Finance - Mathematical Finance
- E-Print:
- International Journal of Theoretical and Applied Finance Vol. 25, No. 01, 2250005 (2022)