# Guaranteed minimum withdrawal benefits with high-water mark fee structure

## TL;DR

This paper introduces a new fee structure for GMWBs using high-water mark principles and models pricing and risk using advanced financial techniques.

## Contribution

The paper introduces a novel high-water mark fee structure and regime-switch jump-diffusion model for GMWB pricing and risk management.

## Key findings

- The HWM-based fee structure improves pricing accuracy under varying market conditions.
- The regime-switch jump-diffusion model effectively captures market volatility for GMWB valuation.
- VaR and CTE metrics provide insights into capital requirements for managing GMWB risks.

## 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.