From Libor to alternative risk-free rates: the transition from the Libor Market Model to the Forward Market Model

This thesis investigates the transition from the Libor Market Model (LMM) to the Forward Market Model (FMM) as developed by Mercurio and Lyashenko. The study outlines the conversion process from Libor rates to alternative risk-free rates, providing the necessary background and motivation behind this shift in financial modeling frameworks. It offers an examination of the Libor Market Model, focusing on its structure, underlying assumptions, calibration techniques and its problematic aspects after the context of post-crisis market adjustments. Then the Forward Market Model is analyzed (under the the Normal and Lognormal specifications), highlighting its dynamics and its advantages over the LMM. The thesis employs FMM Normal specification to value and calibrate the model to cap derivatives using the backward-looking forward rates dynamics derived from the Forward Market Model framework. The results underscore the practical implications of the transition and provide insights into calibration techniques and model performance.