Demographic risk in deep-deferred annuity valuation

A deep-deferred annuity is a deferred annuity where payments start very late in life, i.e. well after the normal retirement age. This annuity has received much attention lately as it was made accessible to 401(k) plans in the United States in 2014. By transferring the risk of outliving retirement savings at high ages to annuity providers, deep-deferred annuities provide annuitants with enhanced later-life financial security. However, the valuation of this annuity suffers from high uncertainty because the mortality data at high ages are sparse and possibly unreliable. In this paper, we use risk ratio to measure demographic risk in the valuation. Demographic risk is decomposed into the following four components: (1) mortality tail curve risk, (2) mortality improvement model risk, (3) parameter risk in mortality tail curves, and (4) parameter risk in mortality improvement rate models. Our quantitative analysis aims to provide insights into the development and risk management of deep-deferred annuities.