  In this article we develop a method for the strong approximation of
stochastic differential equations (SDEs) driven by L\'evy processes or general
semimartingales. The main ingredients of our method is the perturbation of the
SDE and the Taylor expansion of the resulting parameterized curve. We apply
this method to develop strong approximation schemes for LIBOR market models. In
particular, we derive fast and precise algorithms for the valuation of
derivatives in LIBOR models which are more tractable than the simulation of the
full SDE. A numerical example for the L\'evy LIBOR model illustrates our
method.
