Deferred Annuity Contracts under Stochastic Mortality and Interest Rates : Pricing and Model Risk Assessment

Annuity contracts transfer the risk of an individual outliving available assets to aninsurance company. Thus, the insurance company has to value and manage longterm risks. Interest rate risk and longevity risk are the two most important risks forannuity providers. In this paper, we develop a framework to evaluate deferred lifeannuities with stochastic mortality and stochastic interest rate dynamics. We thenstudy the impact of model risk on valuation. An important result of this paper isthe considerable risk potential due to random fluctuations and systematic deviationsfrom the assumptions about interest rate dynamics and mortality dynamicsover a long time period.