LIBOR market models (LMMs) are widely used to valuate interest rate dependent options and guarantees. Currently these models are also applied by life insurance companies to calculate market consistent values of (very) long term contracts with embedded financial options or guarantees. However, in the long term modeling context, LMMs generally suffer from blow-up, i.e. explosion of rates. With the motivation of reducing the blow-up probability we introduce a mean-field extension of LIBOR market models (MF-LMMs). This talk will be about background and motivation for MF-LMMs, existence and uniqueness, various calibration options and numerical results.
Link to the preprint: https://arxiv.org/abs/2109.10779