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Valuation of general GMWB annuities in a low interest rate environment
- Source :
- Insurance: Mathematics and Economics, 2023, 112: 142-167
- Publication Year :
- 2022
-
Abstract
- Variable annuities with Guaranteed Minimum Withdrawal Benefits (GMWB) entitle the policy holder to periodic withdrawals together with a terminal payoff linked to the performance of an equity fund. In this paper, we consider the valuation of a general class of GMWB annuities, allowing for step-up, bonus and surrender features, taking also into account mortality risk and death benefits. When dynamic withdrawals are allowed, the valuation of GMWB annuities leads to a stochastic optimal control problem, which we address here by dynamic programming techniques. Adopting a Hull-White interest rate model, correlated with the equity fund, we propose an efficient tree-based algorithm. We perform a thorough analysis of the determinants of the market value of GMWB annuities and of the optimal withdrawal strategies. In particular, we study the impact of a low/negative interest rate environment. Our findings indicate that low/negative rates profoundly affect the optimal withdrawal behaviour and, in combination with step-up and bonus features, increase significantly the fair values of GMWB annuities, which can only be compensated by large management fees.<br />Comment: Revised version (39 pages, 10 figures), including supplementary material
- Subjects :
- Quantitative Finance - Pricing of Securities
65C20, 91G05, 91G20, 91G30, 91G60
Subjects
Details
- Database :
- arXiv
- Journal :
- Insurance: Mathematics and Economics, 2023, 112: 142-167
- Publication Type :
- Report
- Accession number :
- edsarx.2208.10183
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.insmatheco.2023.07.003