Mean Field Extension of LIBOR Market Model

For the market consistent valuation of long term guarantees LMMs play an important role in life insurance. Originally, these models have been developed to valuate interest rate derivatives over a moderate time horizon. This is a bit in contrast to their application in insurance. Sometimes this particular long-term usage leads to the so-called "blow-up or explosion problem" which emerges when using  MC-methods for the valuation of cash-flows (a significant number of generated paths exhibit unrealistically high realizations of interest rates, such that they can hardy be used).

We present a modification of the LMM which is based on mean-field SDEs and able to cope with the aforementioned problem. Our results cover theoretical questions of existence of the involved processes and practical issues such as calibration and simulation.