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Out-of-Model Adjustments of Variable Annuities

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  • Zhiyi Shen

Abstract

This paper studies the model risk of the Black-Scholes (BS) model in pricing and risk-managing variable annuities motivated by its wide usage in the insurance industry. Specifically, we derive a model-free decomposition of the no-arbitrage price of the variable annuity into the BS model price in conjunction with three out-of-model adjustment terms. This sheds light on all risk drivers behind the product, that is, spot price, realized volatility, future smile, and sub-optimal withdrawal. We further investigate the efficacy of the BS-based hedging strategy given the market diverges from the model assumptions. We disclose that the spot price risk can always be eliminated by the strategy and the hedger's cumulative P\&L exhibits gradual slippage and instantaneous leakage. We finally show that the pricing, risk and hedging models can be separated from each other in managing the risks of variable annuities.

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  • Zhiyi Shen, 2022. "Out-of-Model Adjustments of Variable Annuities," Papers 2208.12838, arXiv.org.
    • Handle: RePEc:arx:papers:2208.12838
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    References listed on IDEAS

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    1. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
    2. Zhiyi Shen & Chengguo Weng, 2020. "Pricing bounds and bang-bang analysis of the Polaris variable annuities," Quantitative Finance, Taylor & Francis Journals, vol. 20(1), pages 147-171, January.
    3. Parsiad Azimzadeh & Peter A. Forsyth, 2015. "The existence of optimal bang-bang controls for GMxB contracts," Papers 1502.05743, arXiv.org, revised Nov 2015.
    4. Christian Knoller & Gunther Kraut & Pascal Schoenmaekers, 2016. "On the Propensity to Surrender a Variable Annuity Contract: An Empirical Analysis of Dynamic Policyholder Behavior," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(4), pages 979-1006, December.
    5. Thorsten Moenig & Daniel Bauer, 2016. "Revisiting the Risk-Neutral Approach to Optimal Policyholder Behavior: A Study of Withdrawal Guarantees in Variable Annuities," Review of Finance, European Finance Association, vol. 20(2), pages 759-794.
    6. Chen, Z. & Vetzal, K. & Forsyth, P.A., 2008. "The effect of modelling parameters on the value of GMWB guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 165-173, August.
    7. Yao Tung Huang & Yue Kuen Kwok, 2016. "Regression-based Monte Carlo methods for stochastic control models: variable annuities with lifelong guarantees," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 905-928, June.
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