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On Valuing Participating Life Insurance Contracts with Conditional Heteroscedasticity

机译：论有条件异方差参与人寿保险合同的价值

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摘要

In this paper, we consider a novel approach for the fair valuation of a participating life insurance policy when the dynamics of the reference portfolio underlying the policy are governed by an Asymmetric Power GARCH (APGARCH) model with innovations having a general parametric distribution. The APGARCH model provides a flexible way to incorporate the effect of conditional heteroscedasticity or time-varying conditional volatility and nests a number of important symmetric or asymmetric ARCH-type models in the literature. It also provides a flexible way to capture both the memory effect of the conditional volatility and the asymmetric effects of past positive and negative returns on the current conditional volatility, called the leverage effect. The key valuation tool here is the conditional Esscher transform of Bühlmann et al. (1996, 1998). The conditional Esscher transform provides a convenient and flexible way for the fair valuation under different specifications of the conditional heteroscedastic models. We illustrate the practical implementation of the model using the S&P 500 index as a proxy for the reference portfolio. We also conduct sensitivity analysis of the fair value of the policy with respect to the parameters in the APGARCH model to document the impacts of different conditional volatility models nested in the APGARCH model and the leverage effect on the fair value. The results of the analysis reveal that the memory effect of the conditional volatility has more significant impact on the fair value of the policy than the leverage effect.
机译：在本文中，当参保人寿保险单所依据的参考投资组合的动态受非对称幂GARCH（APGARCH）模型（具有具有一般参数分布的创新）控制时，我们考虑了一种合理的参保人寿保单公平估值方法。 APGARCH模型提供了一种灵活的方法来合并条件异方差或随时间变化的条件波动性的影响，并且在文献中嵌套了许多重要的对称或非对称ARCH型模型。它还提供了一种灵活的方式来捕获条件波动的记忆效应和过去的正负收益对当前条件波动的非对称效应，称为杠杆效应。这里的关键估值工具是Bühlmann等人的条件Esscher变换。 （1996，1998）。有条件的Esscher变换为有条件的异方差模型的不同规格下的公平估值提供了方便灵活的方式。我们使用标准普尔500指数作为参考投资组合的代理，说明了该模型的实际实现。我们还针对APGARCH模型中的参数对政策的公允价值进行敏感性分析，以记录嵌套在APGARCH模型中的不同条件波动率模型的影响以及杠杆对公允价值的影响。分析结果表明，条件波动的记忆效应比杠杆效应对政策的公允价值影响更大。

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