We study several approximations for the LIBOR market models presented in [1, 2, 5]. Special attention is payed to log-normal approximations and their simulation by using direct simulation methods for log-normal random fields. In contrast to the conventional numerical solution of SDE's this approach simulates the solution directly at the desired point and is therefore much more efficient. We carry out a path-wise comparison of the approximations and give applications to the valuation of the swaption and the trigger swap. 1 Introduction By far the most important class of traded interest rate derivatives is constituted by derivatives which are specified in terms of LIBOR rates. The LIBOR 1 rate L is the annualized effective interest rate over a forward period [T 1 ; T 2 ] and can be expressed in terms of two zero-coupon bonds B 1 and B 2 with face value $1; maturing at T 1 and T 2 ; respectively, L(t; T 1 ; T 2 ) := B1 (t) B2 (t) \Gamma 1 T 2 \Gamma T 1 ; (1) where as usual T 2 is..
