Pricing Equity-Indexed Annuities

According to the fifth census,our country had entered the aged social.With the increasing depth of social aging,more and more problems show up,especially how to provide for the aged.Endowment annuity is a good tool to solve the problem ,but elementary pension which provide basic resource for life can't satisfy their further needs.So business pension have much space.Insurance companies offer traditionally annuities and invest their premium incomes heavily in bonds to meet their liability obligations.While this strategy had provided a steady cash flow and performed well in the past when interest rates were relatively high,this investment product however has lost its attractiveness in recent years.This is in part due to the gigantic swing in the economy.The financial market in recent years is experiencing a bullish equity market and low interest rate enviroment.This has led actuaries to design a new type of annuity products known as equity-indexed annuities(EIAs).EIAs appeal to investors because they not only offer some of the benefits underlying conventional annuities,they also offer participation in the stock market while limiting downside risk of the stock market. A typical EIA guarantees a minimum return (normally 3%)on a portion of the initial amount invested.In addition to this minimum guarantee,the annuitant receives some participation in the appreciation of a pre-determined stock index such as S&P500.In the article we will use the tools of Brownian motion , Esscher transform ,Black-scholes option pricing to find the participation rate which is under point to point-Asian End index method and under considerating death factor.At last we make analysis about the change of some factors influence on the change of breakeven participation rates.