Guaranteed minimum withdrawal benefits with high-water mark fee structure

Abstract

The Guaranteed Minimum Withdrawal Benefit (GMWB), an adjunct incorporated within variable annuities, commits to reimbursing the entire initial investment regardless of the performance of the underlying funds. While extensive research exists in financial and actuarial literature regarding the modeling and valuation techniques of GMWBs, much of it is founded on a static fee structure. Our study introduces an innovative fee structure based on the high-water mark (HWM) principle and a regime-switch jump-diffusion model for the pricing of GMWBs, employing numerical solutions through the Monte Carlo method for solving the stochastic differential equation (SDE). Furthermore, a companion piece of research addresses the risk management of GMWBs within the same analytical framework as the pricing component, an aspect that has received limited attention in the existing literature. In assessing the necessary capital reserves for unforeseen losses, our methodology involves the computation of two risk metrics associated with the tail distribution of net liability from the insurer’s perspective, Value-at-Risk (VaR) and Conditional-Tail-Expectation (CTE). Comprehensive numerical results and sensitivity analyses are also provided.