Index-based hedging solutions are used to transfer the longevity risk to the capital markets. However, mismatches between the liability of the hedger and the hedging instrument cause longevity basis risk. Therefore, an appropriate two-population model to measure and assess longevity basis risk is required. In this study, we aim to construct a two-population mortality model to provide an effective hedge against the basis risk. The reference population is modelled by using the Lee-Carter model with the renewal process and exponential jumps, and the dynamics of the book population are specified. The analysis based on the U.K. mortality data indicates that the proposed model for the reference population and the common age effect model for the book population provide a better fit compared to the other models considered in the study. Different two-population models are used to investigate the impact of sampling risk on the index-based hedge, as well as to analyse the risk reduction regarding hedge effectiveness. The results show that the proposed model provides a significant risk reduction when mortality jumps and sampling risk are taken into account.