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 an insur-ance company. Thus, the insurance company has to value and manage long term risks. Interest rate risk and longevity risk are the two most important risks for annuity providers. In this paper, we develop a framework to evaluate deferred life annuities with stochastic mortality and stochastic interest rate dynamics. We then study the impact of model risk on valuation. An important result of this paper is the considerable risk potential due to random fluctuations and systematic deviations from the assumptions about in-terest rate dynamics and mortality dynamics over a long time period.