Valuation of life-insurance contracts with multiple benefits under stochastic mortality: A QP-Rule framework in light of COVID-19

Abstract

This paper examines the valuation of a life insurance contract combining a Guaranteed Minimum Income Benefit (GMIB), a surrender benefit, and a death benefit under stochastic mortality and financial risks. Building on the established QP-rule valuation approach and a hybrid financial-market framework, we derive analytical valuation formulas adapted to the GMIB contract structure, in which the accumulated fund is converted into a stream of guaranteed annuity payments rather than a single maturity benefit. We then investigate the actuarial implications of alternative stochastic mortality specifications, considering discrete- and continuous-time models with and without jumps. Using UK mortality data, each model is calibrated over a pre-pandemic period ending in 2019 and an extended period ending in 2022 to examine how incorporating the 2020–2022 pandemic-period mortality experience affects benefit and contract values. The numerical analysis also assesses the sensitivity of these values to key contract and surrender parameters.