  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 the longevity basis risk is
required. In this paper, we aim to construct a two-population mortality model
to provide an effective hedge against the longevity basis risk. The reference
population is modelled by using the Lee-Carter model with the renewal process
and exponential jumps proposed by \"Ozen and \c{S}ahin (2020) and the dynamics
of the book population are specified. The analysis based on the UK 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 paper. Different two-population models
are used to investigate the impact of the 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 the sampling risk are taken into account.
