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Description:
The LIBOR Market Model (LMM or BGM) has become one of the most popular
models for pricing interest rate products. It is commonly believed that Monte-Carlo simulation is the only viable method available for the LIBOR Market Model. In this article, however, we propose a lattice/tree (BGM tree or BGM lattice) approach to price interest rate products within the LIBOR Market Model by introducing a shifted forward measure and several novel fast drift approximation methods. This model should achieve the best performance without losing much accuracy. Moreover, the calibration is almost automatic and it is simple and easy to implement. Adding this model to the valuation toolkit is actually quite useful; especially for risk management or in the case there is a need for a quick turnaround.

Key Words: LIBOR Market Model (LMM or BGM), lattice model, tree model, shifted forward measure, drift approximation, risk management, calibration, callable exotics, callable bond, callable capped floater swap, callable inverse floater swap, callable range accrual swap.