Risk Management of Guaranteed Minimum Benefits Under Regime-Switching Jump-Diffusion Model

In this paper, we focus on pricing and hedging of Guaranteed Minimum Benefits (GMBs) and we extend the existing framework by assuming the underlying asset dynamics evolve under a regime-switching jump-diffusion environment. Two basic GMB contracts, Guaranteed Minimum Maturity Benefit (GMMB) and Guaranteed Minimum Death Benefit (GMDB), are modeled by a quantitative model which assesses both the market risk on the liability side and the revenue risk on the asset side from the viewpoint of insurers. The stochastic mortality parameters are estimated by calibrating to the mortality data of the United States male population. Numeric solutions for net liabilities, fair rate of fees and Greeks (sensitivities of net liabilities with respect to model parameters) of GMMB and GMDB are calculated by an accurate and fast Fourier Space Time-stepping (FST) algorithm. Monte Carlo results are also provided for comparative purpose. An unhedged and three statically hedged portfolios are introduced, and their performances are assessed by comparing their short term and long term volatility, VaR and CVaR. The hedging results provide insurers some guidelines to hedge according to their risk tolerances levels