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Pricing and hedging of variable annuities with state-dependent fees

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  • Delong, Łukasz

Abstract

We investigate the problem of pricing and hedging variable annuity contracts for which the fee deducted from the policyholder’s account depends on the account value. It is believed that state-dependent fees are beneficial to policyholders and insurers since they reduce policyholders’ incentives to lapse the policies and match the costs incurred by policyholders with the pay-offs received from embedded guarantees. We consider an incomplete financial market which consists of two risky assets modelled with a two-dimensional Lévy process. One of the assets is a security which can be traded by the insurer, and the second asset is a security which is the underlying fund for the variable annuity contract. In our model we derive an equation from which the fee for the guaranteed benefit can be calculated and we characterize a strategy which allows the insurer to hedge the benefit. To solve the pricing and hedging problem in an incomplete financial market we apply a quadratic objective.

Suggested Citation

  • Delong, Łukasz, 2014. "Pricing and hedging of variable annuities with state-dependent fees," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 24-33.
    • Handle: RePEc:eee:insuma:v:58:y:2014:i:c:p:24-33
    DOI: 10.1016/j.insmatheco.2014.06.002
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    References listed on IDEAS

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    11. Deelstra, Griselda & Rayée, Grégory, 2013. "Pricing Variable Annuity Guarantees in a local volatility framework," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 650-663.
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    Cited by:

    1. Anne MacKay & Maciej Augustyniak & Carole Bernard & Mary R. Hardy, 2017. "Risk Management of Policyholder Behavior in Equity-Linked Life Insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(2), pages 661-690, June.
    2. Runhuan Feng & Xiaochen Jing & Jan Dhaene, 2015. "Comonotonic Approximations of Risk Measures for Variable Annuity Guaranteed Benefits with Dynamic Policyholder Behavior," Tinbergen Institute Discussion Papers 15-008/IV/DSF85, Tinbergen Institute.
    3. Wang, Gu & Zou, Bin, 2021. "Optimal fee structure of variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 587-601.
    4. Zhenyu Cui & Anne MacKay & Marie-Claude Vachon, 2022. "Analysis of VIX-linked fee incentives in variable annuities via continuous-time Markov chain approximation," Papers 2207.14793, arXiv.org.
    5. Zhou, Jiang & Wu, Lan, 2015. "Valuing equity-linked death benefits with a threshold expense strategy," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 79-90.
    6. Zhou, Jiang & Wu, Lan, 2015. "The time of deducting fees for variable annuities under the state-dependent fee structure," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 125-134.
    7. D. Baños & T. Meyer-Brandis & F. Proske & S. Duedahl, 2017. "Computing deltas without derivatives," Finance and Stochastics, Springer, vol. 21(2), pages 509-549, April.
    8. Michael A. Kouritzin & Anne MacKay, 2017. "VIX-linked fees for GMWBs via Explicit Solution Simulation Methods," Papers 1708.06886, arXiv.org, revised Apr 2018.
    9. Anne Mackay & Marie-Claude Vachon, 2023. "On an Optimal Stopping Problem with a Discontinuous Reward," Papers 2311.03538, arXiv.org, revised Nov 2023.
    10. Kouritzin, Michael A. & MacKay, Anne, 2018. "VIX-linked fees for GMWBs via explicit solution simulation methods," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 1-17.
    11. Anna Rita Bacinello & Ivan Zoccolan, 2019. "Variable annuities with a threshold fee: valuation, numerical implementation and comparative static analysis," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 21-49, June.
    12. Fontana, Claudio & Rotondi, Francesco, 2023. "Valuation of general GMWB annuities in a low interest rate environment," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 142-167.
    13. Moenig, Thorsten, 2021. "Variable annuities: Market incompleteness and policyholder behavior," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 63-78.

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    More about this item

    Keywords

    Quadratic optimization; Incomplete market; Lévy process; Backward stochastic differential equations; Lévy Clayton copula;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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