Value Of Equity- Index Annuity With A Rate Cap

With the arrival of China's population aging, pension problems will become a new and important problem that China faces. In the same time, basic pension can only ensure their basic living standard. It is far from being able to satisfy the needs of their lives. Therefore, the development of commercial annuity insurance is particularly important in our country. However, on one hand, because of its design problems, the traditional annuity insurance is likely to lead to the mismatch between investment incomes in a period and the expected return; on the other hand, it can not find a good solution to solve the influence of inflation to people's life quality. Then this kind of rate-sensitive annuity products appeared. And Equity- Index Annuity (EIA) is one of them.Being a new kind of annuity in the American and European markets, EIA guarantees a minimum rate of return and its equity is related to the performance of a certain stock index. That means it will rise when the market goes up while it will guarantee a minimum rate of return when the market goes down, which makes it very attractive to risk-avoiding investors. How ever, high premium cost blocked the sales of EIA to extent. So how to decrease its premium becomes an important way to increase its sales. In this paper, we will use the method of rate cap to lower premium, provide some pricing formulas, and conduct a numerical simulation to analyze the factors that influence the participation rat. On the other hand traditional assumption for the stock index movement is unreasonable for the brusque variations of the stock index because of the important political or nature even,In this paper, we discuss how to price IEA with a cap rate under the indexing methods of point to point supposed stock index follow jump diffusion process, provide a pricing formula, and conduct a numerical simulation to analyze the factors that influence the participation rat.The structure of this thesis is as follows: The first section introduces what Equity- Index Annuity is, makes a comparison between EIA and the traditional annuity and tells its significance. The second part introduces the preliminary knowledge this thesis needs and some terminologies. The third part introduces how to price EIA with a rate cap under traditional model. This part also has a sensitive test to the factors that influences participation rate. The fourth part gives an introduction how to price EIA with a rate cap under jump diffusion model with a point to point yields calculation method. Also, it has a sensitive test to the factors that influences participation rate.