The LIBOR Market Model Calibration with Separated Approach

From an economic perspective, interest rates constitute key tools for decision making in the financial sector as they have micro and macro impacts, making its risk management a crucial matter. The LIBOR Market Model (LMM) uses the yield curve of the British interbank rate LIBOR (forward) as its basic input. Unlike models that use instantaneous rates, those involved in the LMM are observable in the market. Furthermore, the model is consistent with and adjusts its parameters according to the option valuation on futures formula in the Black ‘76 fashion. This allows for efficient calibration and can be used to value various derivative financial instruments. While there are several approaches for calibration, this work uses the separated approach with optimization. It is implemented using a routine in MATLAB with data of european swaptions. This work concludes that the proposed algorithm is computationally efficient and the fit is satisfactory.