Pricing Equity-indexed Annuities Under The Multi-factors

Along with the global aging, our country population projections suggest thatChina’s age structure type not only switch to agedness from adult, but also will developto high aging in the coming decades. So the traditional annuity products have alreadycan’t satisfy people’s demand for high return on investment, and also need to find waysto ease the major issues of the future aging. Against the current situation, equity-indexedannuity is released from insurance companies between fixed annuity and variableannuity. It is a kind of live gold, and also a kind of interest sensitive annuity products.Equity-indexed annuity is popular since its released. It depends on the minimumguarantee profits, and it is associated with a certain stock or bond index returns.Equity-indexed annuity has a strong appeal for those who are afraid of market risk andwant to earn profits from the stock market growth. As the same time, the policy holderis at a certain rate participate in the growth of the stock index, and the rate of the rate isthe participation rate. So making sure reasonable participation rate has significantinfluence on annuity products’ design. This article is mainly based on the pricingformula of equity-indexed annuity in the Tiong(2000), and series of research on thebasis of pricing equity-indexed annuity by Qian Linyi. We consider the multi-factors tousing simple point to point method, annual reset method, high water mark method andAsian-end method respectively to explore the pricing of equity-indexed annuity underthe Esscher transform.This paper is structured as follows: The first section mainly describes the definitionof equity and equity-indexed annuities, and the method of computing index returns rate.Points out the influence of old-age insurance system with the aging in our country.Made related research summary of equity-indexed annuity at home and abroad. Thesecond part mainly describes the representative stock index on the finance market of theworld and our country. And introduce the related preliminary knowledge of thestochastic process, risk neutral theorem, B-S pricing model and equivalent martingalemeasure. Of course, these are paved for the back of the pricing formula.The third partmainly introduces the pricing of equity-indexed annuities under the fractional Brownianmotion with stochastic mortality risk, the regime-switching jump diffusion. Usingsimple point to point method, annual reset method, high water mark method andAsian-end method respectively computes index returns rate of equity-indexed annuity. And price the equity-indexed annuity under the corresponding method. The fourth partmainly respectively describes the four conmmon method of computing index returnsrate on the above, assume some parameter values according to the pricing formula, andanalysis of the another parameters to the influence of the break even participate rate.The fifth part is mainly summarized and prospected the study of equity-indexed annuity.