On Valuing Participating Life Insurance Contracts with Conditional Heteroscedasticity

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