Out-of-Model Adjustments of Variable Annuities

Zhiyi Shen

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arXiv · 2208.12838

Out-of-Model Adjustments of Variable Annuities

Zhiyi Shen

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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. 2022-08-26. Out-of-Model Adjustments of Variable Annuities. https://arxiv.org/abs/2208.12838

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