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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Accesso online: | https://arxiv.org/abs/2605.30567 |
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| _version_ | 1866917554788761600 |
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| author | Molent, Andrea |
| author_facet | Molent, Andrea |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30567 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Valuation of GLWB-LTC Annuities with Lévy Equity Dynamics, Stochastic Interest Rates and Health-State Transitions Molent, Andrea Pricing of Securities 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. |
| title | Valuation of GLWB-LTC Annuities with Lévy Equity Dynamics, Stochastic Interest Rates and Health-State Transitions |
| topic | Pricing of Securities |
| url | https://arxiv.org/abs/2605.30567 |