Guaranteed minimum income benefit valuation via a numéraire transformation approach

Abstract Owing to their innovative guarantee features, the popularity of variable annuities has gained significant traction as suitable retirement products in recent years. Amongst these guarantees, the guaranteed minimum income benefit (GMIB) stands out as an appealing rider that can be integrated into variable annuity contracts. In this research, we construct a comprehensive modelling framework that encompasses three sources of uncertainty, namely interest risk, mortality risk and investment risk, with the aim of valuing the GMIB. These risk factors are modelled stochastically whilst accounting for the interdependence between interest and mortality risks. The numéraire transformation technique is utilised in our approach, capitalising on the concepts of the forward and endowment-risk-adjusted measures. By considering two distinct settings of the Benefit Base functions, we derive an analytic solution for the GMIB. Our numerical findings demonstrate the superiority of our proposed methodology vis-á-vis the standard Monte Carlo simulation as a benchmark in terms of computational accuracy and efficiency, achieving a remarkable average improvement of 99% computing time reduction compared to the benchmark. Furthermore, we conduct an extensive sensitivity analysis to explore the levels of impact of various model parameters on the value of the GMIB.