Pricing and Hedging of Guaranteed Minimum Benefits Under Regime-Switching and Stochastic Mortality

Abstract

This paper presents a novel framework for pricing and hedging of the Guaranteed Minimum Benefits (GMBs) embedded in variable annuities (VA) contracts whose underlying mutual fund dynamics evolve under the influence of the regime-switching model. Semi-closed form solutions for prices of various GMBs are derived; pricing and hedging is performed using an accurate, fast and efficient Fourier Space Time-stepping (FST) algorithm, which allows deriving the Greeks required for hedging purposes, as a part for the pricing procedure. The mortality component of the valuation framework is calibrated using Australian mortality data. Sensitivity analysis is performed with respect to various parameters including guarantee levels, time to maturity, interest rates and volatilities. The hedge effectiveness is assessed by comparing profit-and-loss distributions for unhedged, statically and semi-statically hedged portfolios. The results provide a comprehensive analysis on pricing and hedging the longevity risk, interest rate risk and equity risk for the GMBs embedded in VAs, and highlights the benefits to insurance providers who offer those products.