A moneyness-adapting fee structure for guaranteed benefits embedded in variable annuities: Pricing and valuation

Guaranteed minimum death benefit (GMDB) and guaranteed minimum maturity benefit (GMMB) are two common guarantee riders embedded in variable annuities. To cover the financial risks incurring from the guarantees, fees are charged based on the underlying fund value, where a traditional approach funds the guarantees as a constant rate of fee over the period of the accumulation phase. This fee structure, however, potentially encourages surrendering when the options are out-of-money. To prevent the adverse incentives, Bernard et al. (2014) introduced a state-dependent fee, where fees are charged only when the guarantees are in-the-money or close to being in-the-money. This project proposes a moneyness-adapting fee structure, aiming to further reduce the insurer’s reserve. Following the estimation of rate of fee charged for GMDB and/or GMMB under three pricing principles, the performances of three fee structures are compared with numerical illustrations, based on the measures of value-at-risk and conditional-tail-expectation.