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

Area of Science:

• * Actuarial Science
• * Financial Mathematics
• * Risk Management

Background:

• * Variable annuities often include Guaranteed Minimum Withdrawal Benefits (GMWBs) that protect the initial investment.
• * Existing GMWB research primarily uses static fee structures.
• * Limited attention has been given to GMWB risk management within pricing frameworks.

Purpose of the Study:

• * To develop an innovative fee structure for GMWBs based on the high-water mark (HWM) principle.
• * To price GMWBs using a regime-switch jump-diffusion model and Monte Carlo methods.
• * To analyze the risk management of GMWBs, focusing on capital reserve estimation.

Main Methods:

• * Implemented a high-water mark (HWM) fee structure.
• * Utilized a regime-switch jump-diffusion model for pricing.
• * Employed Monte Carlo simulations to solve the stochastic differential equation (SDE).
• * Calculated Value-at-Risk (VaR) and Conditional-Tail-Expectation (CTE) for risk assessment.

Main Results:

• * Developed a novel GMWB pricing model with a dynamic fee structure.
• * Provided a framework for assessing insurer capital reserves against GMWB liabilities.
• * Demonstrated the utility of VaR and CTE in quantifying tail risk.

Conclusions:

• * The proposed HWM fee structure and regime-switch model offer a more realistic approach to GMWB pricing.
• * The study provides essential tools for insurers to manage GMWB risks effectively.
• * Enhanced risk assessment through VaR and CTE supports robust capital allocation.