Risk management of guaranteed minimum maturity benefits under stochastic mortality and regime-switching by Fourier space time-stepping framework

This paper presents a novel framework for valuation and hedging of the insurer's net liability on a Guaranteed Minimum Maturity Benefit (GMMB) embedded in variable annuity (VA) contracts whose underlying mutual fund dynamics evolve under the influence of the regime-switching model. Numerical solutions for valuations and Greeks (i.e. valuation sensitivities with respect to model parameters) of GMMB under stochastic mortality are derived. Valuation and hedging is performed using an accurate, fast and efficient Fourier Space Time-stepping (FST) algorithm. The mortality component of the model is calibrated to the American male population. Sensitivity analysis is performed with respect to various parameters. The hedge effectiveness is assessed by comparing profit-and-loss performances for an unhedged and three statically hedged portfolios. The results provide a comprehensive analysis on valuation and hedging the longevity risk, interest rate risk and equity risk for the GMMB embedded in VAs, and highlight the benefits to insurance providers who offer those products.