Return distributions of equity-linked retirement plans under jump and interest rate risk

We consider a savings plan, where the paid capital is guaranteed at time of retirement, in the German market available as Riester-Rente and supported by federal cash payments and tax benefits. We generalize several capital guarantee mechanisms to payment plans and compare their distribution: the return distribution of a classical insurance strategy with investments in the actuarial reserve fund, a CPPI strategy, and a Stop Loss strategy, in optimistic, standard and pessimistic market scenarios. To model the distribution we use a jump diffusion process parameterized to resemble the MSCI World index for the stock investment and a Hull-White Extended Vasicek process, calibrated to the euro zero-bond curve, for the risk free investment. We also analyze how fee structures and gap risk affect the performance of these savings plans. Additionally, we present a very simple parameter estimation method for this kind of simulation studies.