Insurance products with guarantees in an affine setting

Abstract

Medium- and long-term insurance products must participate in equity market returns to remain competitive. To eliminate downside risk, guarantees should be included, which naturally gives rise to the problem of valuing contracts in a unified insurance-finance framework. We study a general setup that allows for joint modelling of financial markets, mortality, and policy holder behaviour. Within this framework, we propose a general affine approach exploiting the tractability of affine processes to obtain explicit valuation formulas for variable annuities and related contracts. The model permits flexible dependence between mortality and equity dynamics. Moreover, surrender intensities are modelled as functions of the driving affine process, thereby introducing endogenous market dependence into lapse behaviour – a feature rarely treated analytically in the literature. The resulting framework combines analytical tractability with sufficient flexibility to capture key features of long-term insurance products.