Insurance products with guarantees in an affine setting

Abstract

To make medium- and long-term insurance products attractive, it is essential to enable participation in stock market returns. However, to eliminate downside risk, guarantees must be included, which naturally leads to the challenge of valuing such contracts within a unified insurance-finance framework. We develop a general setup that allows for the joint modelling of financial markets, mortality and policyholder behaviour. Within this framework, we propose a general affine approach and derive explicit valuation formulas for variable annuities and related contracts, while retaining computational tractability due to the affine structure. The model permits flexible dependence between mortality and equity dynamics, as supported by empirical evidence from the COVID-19 pandemic. Moreover, surrender intensities are modelled as functions of the underlying affine process, thereby introducing market dependence into lapse behaviour. The resulting framework combines analytical tractability with sufficient flexibility to capture key features of long-term insurance products.