Journal Article

Guaranteed Annuity Option Under Correlated and Regime-Switching Risks

Grozen, Jude Martin B., Mamon, Rogemar S.

2026

Overview

Guaranteed annuity options (GAOs) allow policyholders to convert accumulated funds into life annuities at maturity at a guaranteed minimum rate. Thus, insurers are exposed to both investment and longevity risks. Accurate valuation of these long-term, survival-contingent contracts is essential for solvency assessment and risk management. Many existing approaches assume independence between interest rate and mortality risks. This paper develops a computationally efficient pricing framework for GAOs that jointly models interest and mortality rates as correlated stochastic processes with regime-switching dynamics governed by a finite-state continuous-time Markov chain. Model parameters are estimated using U.S. interest rates and cohort mortality data via quasi-maximum likelihood estimation. A semi-analytic valuation formula is derived based on the joint distribution of the underlying processes. Numerical results show that incorporating correlation and regime-switching materially increases GAO prices relative to conventional one-state models. The proposed semi-analytic approach delivers substantial computational advantages over standard Monte Carlo simulations. Sensitivity analysis further identifies the parameters most relevant for long-horizon pricing and solvency considerations. This highlights the practical relevance of the framework for managing longevity-linked guarantees under economic and demographic uncertainty.

• Publisher: MDPI AG
• Subject: Annuities / Economic growth / Insurance premiums / Interest rates / Life expectancy / longevity risk / Macroeconomics / Markov analysis / Markov processes / Monte Carlo method / Mortality / Pandemics / pension design / Policyholders / regime-switching models / Retirement income / Risk management / semi-analytic valuation / Solvency / Stochastic models / Trends / Valuation / Volatility