Solvency analysis of deferred annuities

While the solvency analysis of immediate life annuity portfolios has been extensively studied, the case of deferred annuities has received comparatively much less attention. We assess the importance and effect of stochastic mortality models and interest rates on the solvency analysis of a portfolio of deferred annuity contracts. Our analysis considers three steps: first, the benchmark case where mortality rates and interest rates are both deterministic; then, the case in which only mortality rates are stochastic is explored; finally, the full model where both mortality rates and interest rates are stochastic. The results demonstrate the model risk stemming from the uncertainty in the mortality models and its impact on the evaluation of solvency margins for life annuities. The role of the deferment period is thoroughly discussed and compared to the case of immediate annuities.