This study proposed and evaluated a new insurance product, i.e., the variable annuity product, accompanied by the health status and the guaranteed lifelong withdrawal benefit (GLWB). Due to specific problems, the insurance sector is now one of the riskiest industries. The aging of the population and rising medical service costs as a result of technological advancements are to blame for this. Thus one of the most basic needs in the health insurance sector is to design an innovative product. In this article, a mixed discrete-continuous time model is proposed to calculate the fair fee of the product, calculated using equilibrium condition between premium and benefits. We considered constant volatility and rate of interest along with health status benefits and hospitalization coverage. For an illustration of the capability of this product and some possible improvements in the product, a numerical study, and sensitivity analysis have been conducted. The results showed that the withdrawal amount and age have a significant impact on the cost. A rise in the initial insured age and withdrawal amount increases the fair fee of the product. The GLWB rider’s guaranteed amount and medical expenses are included in the withdrawal amount.
This study investigates the pricing problem of a variable annuity (VA) contract embedded with a guaranteed lifetime withdrawal benefit (GLWB) rider. VAs are annuities in which the value is linked to a bond and equity sub‐account fund. The guaranteed lifetime withdrawal benefit rider regularly provides a series of payments to the policyholder for the term of the policy while he/she is alive, regardless of portfolio performance. At the time of the policyholder's death, the remaining fund value is given to his nominee. Therefore, proper fund modeling is critical in the pricing of VA products. Several writers in the literature used a GBM model in which variance is considered to be constant to represent the fund value in a variable annuity contract. However, on the other hand, the returns on financial assets are non‐normally distributed in real life. A bit much Kurtosis, leverage effect, and Non‐zero Skewness characterize the returns. The generalized autoregressive conditional heteroscedastic (GARCH) models are also used for presenting a discrete framework for the pricing of GLWB. Still, the interest rate was kept constant without including the surrender benefit and the static withdrawal approach, which keeps the model far from the real scenario. Thus, in this research, the generalized GARCH models are used with surrender benefit and dynamic withdrawal strategy to develop a time series model for the pricing of annuity that overcomes the constraints of previous models. A numerical illustration and sensitivity analysis are used to examine the suggested model.
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