Pricing lifelong guarantees: mixed-exponential jump-diffusion risks

Abstract This paper focuses on the pricing of lifelong guarantees, to provide a stream of lifetime income in a Variable Annuity contract, mitigating both longevity and market downside risks. The dynamics of the risky assets is described by a Mixed-Exponential Jump-Diffusion model to effectively capture key empirical characteristics of asset returns, including high kurtosis and leverage effects. The pricing problem is assessed with and without the surrender option. A sensitivity analysis is presented to investigate the different models studied and some numerical illustrations are provided.