We present a computational methodology to value and hedge long term zero-coupon bonds trading in short and medium term ones. For this purpose we develop a discrete time stochastic yield curve model with limited availability of maturity dates at a fixed time point and newly issued bonds at future time points. This involves reinvestment risk and there is no perfect hedging strategy available for long term liabilities. We calibrate the model to market data and describe optimal hedging strategies under a given risk tolerance. These considerations provide a natural extrapolation of the yield curve beyond the last liquid maturity date, and a framework which allows to value long term insurance liabilities, for instance, under Solvency 2. Moreover, we determine the optimal trading strategy replicating the liabilities under the given risk tolerance.