  The LIBOR market model is very popular for pricing interest rate derivatives,
but is known to have several pitfalls. In addition, if the model is driven by a
jump process, then the complexity of the drift term is growing exponentially
fast (as a function of the tenor length). In this work, we consider a
L\'evy-driven LIBOR model and aim at developing accurate and efficient
log-L\'evy approximations for the dynamics of the rates. The approximations are
based on truncation of the drift term and Picard approximation of suitable
processes. Numerical experiments for FRAs, caps, swaptions and sticky ratchet
caps show that the approximations perform very well. In addition, we also
consider the log-L\'evy approximation of annuities, which offers good
approximations for high volatility regimes.
