Valuation of GLWB-LTC Annuities with L\'evy Equity Dynamics, Stochastic Interest Rates and Health-State Transitions

Andrea Molent

Papers from arXiv.org

Abstract: This paper develops a valuation framework for guaranteed lifetime withdrawal benefit (GLWB) contracts with long-term care (LTC) features when the reference fund follows exponential Levy dynamics and the short rate follows the Hull-White model. The contract combines financial guarantees, longevity protection, health-contingent LTC payments, and surrender optionality, requiring the joint treatment of jump risk, stochastic discounting, and disability risk. The numerical method couples a recombining Hull-White trinomial tree with an implicit-explicit (IMEX) finite difference scheme. The framework incorporates a seven-state health model, annual fees, LTC payments, guaranteed withdrawals, and bang-bang policyholder actions, and is benchmarked against Monte Carlo simulation. Numerical results show that the hybrid tree-IMEX method delivers stable long-maturity prices consistent with simulation benchmarks. They also show that Levy equity dynamics and stochastic interest rates have a material impact on fair fees and surrender incentives, and affect the decomposition of contract value. The findings highlight the importance of modelling financial tail risk and interest-rate risk jointly when pricing long-term insurance guarantees with LTC-contingent benefits.

Date: 2026-05, Revised 2026-06
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