The Pricing Of Equity-Index Annunity Under Two Conditions

Equity indexed annuity is a kind annuity with the minimum guar-antee of income, which can guarantee the capital and earnings against loss. Meanwhile, on the basis of minimum guarantee, the yield of the actual annuity paid to customers is relevant to the index of the prescribed stocks or bonds. Because equity indexed annuity can get involved in the development of the capital market without the risk of market downturn, it remains popular among customers with low tolerance towards risk and passionate about getting involved in the market since it was launched.Firstly, this paper introduces the related concepts of equity indexed annuity, tells us the indexing methods of equity indexed annuity. Sec-ondly, on the basis of Serena Tiong’s study, we think about the pricing of equity indexed annuity under the risk of death. We use the meth-ods of point to point and annual reset to elicit the pricing formula. Finally, the equity index is often assumed within the Black-Scholes framework, but some rare events (for instance, the unexpected finan-cial events, crucial political changes or financial storms) will lead to abrupt price changes. This article assumes that equity indexed annu-ity follows a jump diffusion process and uses the Esscher transform to elicit the pricing formula.