The Study Of Pricing The Equity Index Annuity Based On The Longevity Risk Index

The Equity Index Annuity (EIA) has developed rapidly since it was released in American capital markets. As a kind of index annuity, EIA is essentially a kind of deferred annuity. It guarantees a minimum rate of interest on the investment and protects the policyholders from the loss of the principal and income on investment. At the same time,besides the minimum rate of interest on the investment,the profit rate it actually pays to the policyholders is associated with the stock index or bond index. After about twenty years of development,its applications in actuarial pricing and risk theory appear more and more important.Given that with the rapid growth of the economy and the consistent improvement of medical conditions, the mortality declines sharply, which leads to the appearance of longevity risk directly.Whether the longevity risk can be evaded, the core is relied on the mortality forecasting and the annuity which is linked with longevity risk pricing.Based on the pricing of EIA and the forecasting of mortality under longevity risk,this paper intents to discuss the pricing of EIA under the assumption of mortality with jump diffusion and the correlation between different groups. In the process of the pricing, the key difference of this paper lies in:Among the previous researches of some scholars the basic assumption of the pricing is that the mortality is a constants or follow a continuous time process, while the basic assumption in this paper is that: One is that the mortality follow a jump diffusion process, because the occurrence of some emergencies such as earthquake and tsunami will certainly influence the mortality and the variety of mortality will affect the pricing of EIA directly; the other is that the mortality between different groups is indeed relational and not independent absolutely. Then we conduct the sensibility analysis with the factors which affect the participation rate such as guaranteed interest rate and deferred period under the new model, and do the comparative analysis with the classic Lee-Carter model. And we conclude that the new models are more suitable for pricing the EIA because they reflect the influence of mortality more accurately. Finally, this paper gives the conclusion and prospect.