Pricing Model Study On Guaranteed Lifelong Withdrawal Benefit In Variable Annuity

With a rapidly aging population, China has stepped into an era of great pension pressure, which also creates huge market for pension products. Compared to western countries, there is still a huge gap in pension insurance products in China. With a single variety, our pension insurance products are unable to meet the future needs of the national pension. Enriching the varieties of commercial annuity is undoubtedly an important way to alleviate the pressure. Variable annuity is well developed and has become the mainstream in the western pension markets. Guaranteed lifelong withdrawal benefit(GLWB) in variable annuity is the current best seller of all variable annuity products in western markets. However, China hasn't introduced the GLWB into the life insurance market, while researches and literature on GLWB in variable annuity are less, which results in a strong application value and practical significance of this paper.This paper firstly introduces the concept and features of several common provision of GLWB, and at the same time, presents the GLWB's numerical demonstration and analyzes the interest rate risk and mortality risk of GLWB. Starting with the research in characteristics of GLWB, this paper decomposes GLWB into two parts:lifetime annuity and path-dependent put option of a personal account value to price GLWB, namely pricing on GLWB is equivalent to add the present value of the above two together. First of all,paper constructs the pricing model of GLWB at a predetermined interest rate and mortality. The interest rates and mortality will change greatly considering of the longevity of GLWB products. Therefore, the predetermined interest rate and a predetermined mortality can't well simulate the real economic and social situation. Instead of a fixed interest rate and fixed mortality, the paper introduces Vasicek model which describes stochastic interest rate models and mean reversion with jumps Feller stochastic process describing stochastic mortality model to build GLWB pricing model. Finally, the Monte Carlo simulation method is used to analyze the guarantee fair rates comparatively in different interest rate and mortality assumptions and meanwhile analyze the influence to guarantee fair rates form the withdrawal rate, the insured age, underlying asset volatility, stochastic interest rate model parameters, stochastic mortality model parameters and etc. The paper is of great building significance and research value to the launch of GLWB products on variable annuity market in China.