Optimal static hedging of variable annuities with volatility-dependent fees

Variable annuities (VAs) and other long-term equity-linked insurance products are typically difficult to hedge in the incomplete markets. A state-dependent fee tied with market volatility for VAs is designed to contribute the risk-sharing mechanism between policyholders and insurers. Different from prior research, we discuss several aspects on a fair valuation, fee-rate determination and hedging with volatility-dependent fees from the perspective of a VA hedger. A method of efficient hedging strategy as a benchmark compared to other strategies is developed in the stochastic volatility setting. We illustrate this method in guaranteed minimum maturity benefits (GMMBs), but it is also applicable to other equity-linked insurance contracts.