Valuation and optimal surrender of variable annuities with guaranteed minimum benefits and periodic fees

Kirkby, Justin; Aguilar, Jean-Pierre

doi:10.1080/03461238.2022.2141656

Cited by 9 publications

(2 citation statements)

References 92 publications

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“…The notable finding was that the optimal fee structure took on a barrier-type form with a time-dependent free boundary, assuming a no-surrender scenario. On the other hand, Kirkby and Aguilar [ 20 ] investigated the valuation and optimal surrender dynamics of variable (equity-linked) annuities within a Lévy-driven equity market framework. Their analysis incorporated mortality risk and introduced a practical periodic fee structure that could dynamically vary over time, levied as a proportion of the fund value.…”

Section: Introductionmentioning

confidence: 99%

Guaranteed minimum withdrawal benefits with high-water mark fee structure

Han,

Wu,

et al. 2024

PLoS ONE

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The Guaranteed Minimum Withdrawal Benefit (GMWB), an adjunct incorporated within variable annuities, commits to reimbursing the entire initial investment regardless of the performance of the underlying funds. While extensive research exists in financial and actuarial literature regarding the modeling and valuation techniques of GMWBs, much of it is founded on a static fee structure. Our study introduces an innovative fee structure based on the high-water mark (HWM) principle and a regime-switch jump-diffusion model for the pricing of GMWBs, employing numerical solutions through the Monte Carlo method for solving the stochastic differential equation (SDE). Furthermore, a companion piece of research addresses the risk management of GMWBs within the same analytical framework as the pricing component, an aspect that has received limited attention in the existing literature. In assessing the necessary capital reserves for unforeseen losses, our methodology involves the computation of two risk metrics associated with the tail distribution of net liability from the insurer’s perspective, Value-at-Risk (VaR) and Conditional-Tail-Expectation (CTE). Comprehensive numerical results and sensitivity analyses are also provided.

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Section: Introductionmentioning

confidence: 99%

Guaranteed minimum withdrawal benefits with high-water mark fee structure

Han,

Wu,

et al. 2024

PLoS ONE

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“…Kouritzin and MacKay (2018) further assess the effectiveness of the VIX-linked fee structure in decreasing the sensitivity of the insurer's liability to volatility risk for a GMWB contract. While most of the actuarial literature on state-dependent fees are mainly focused on the valuation and surrender analysis of VAs (e.g., Bauer et al (2017); ; Kirkby and Aguilar (2023);MacKay et al (2017MacKay et al ( , 2023 and reference therein), there is quite a limited number of studies on the hedging problem of VAs with state-dependent fees. Delong (2014) considers an incomplete financial market by modeling the dynamics for the account value and the underlying investment asset with a general two-dimensional Lévy process.…”

Section: Introductionmentioning

confidence: 99%

Optimal Static Hedging of Variable Annuities with Volatility-Dependent Fees

Tang

2023

Risks

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Variable annuities (VAs) and other long-term equity-linked insurance products are typically difficult to hedge in the incomplete markets. A state-dependent fee tied with market volatility for VAs is designed to contribute the risk-sharing mechanism between policyholders and insurers. Different from prior research, we discuss several aspects on a fair valuation, fee-rate determination and hedging with volatility-dependent fees from the perspective of a VA hedger. A method of efficient hedging strategy as a benchmark compared to other strategies is developed in the stochastic volatility setting. We illustrate this method in guaranteed minimum maturity benefits (GMMBs), but it is also applicable to other equity-linked insurance contracts.

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Robust time-consistent strategy for the defined contribution pension plan with a minimum guarantee under ambiguity

Hao,

Chang

2023

Comp. Appl. Math.

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Valuation and optimal surrender of variable annuities with guaranteed minimum benefits and periodic fees

Cited by 9 publications

References 92 publications

Guaranteed minimum withdrawal benefits with high-water mark fee structure

Guaranteed minimum withdrawal benefits with high-water mark fee structure

Optimal Static Hedging of Variable Annuities with Volatility-Dependent Fees

Robust time-consistent strategy for the defined contribution pension plan with a minimum guarantee under ambiguity

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