The standard Libor-Forward-Market-Models provides a way of modelling the evolution of forward rates in time. However the model does not seem to be well suited for the modelling of zero-bonds. But ...
I apologize if this is supposed to be obvious, but ... . Libor spot rates are quoted up to a year, beyond that one can use Eurodollar futures to continue to build the curve. Let's say up to 3 years. ...