On Valuing Participating Life Insurance Contracts with Conditional Heteroscedasticity |
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Authors: | Tak Kuen Siu John W Lau Hailiang Yang |
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Institution: | (1) Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA, 6845, Australia;(2) School of Statistics and Actuarial Science, University of the Witwatersrand, Private Bag 3, Johannesburg, WITS 2050, South Africa;(3) Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Kowloon, Hong Kong |
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Abstract: | 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. |
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Keywords: | APGARCH model Conditional Esscher transforms Conditional heteroscedasticity Default option Leverage effect Memoryness Participating life insurance policies |
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