Study Of Equity-Index Annuity Pricing Under Stochastic Interest Rate

Population aging is a process of the proportion of elderly population in totalpopulation rising. It first appeared in France in the1850s, subsequently, many westerndeveloped countries have appeared this phenomenon. According to the relevant UnitedNations Standards, the specific indicator for the population aging is the proportion ofpeople aged60and above in total population reaches10%, or the proportion of peopleaged65and above in total population reaches7%. Under this standard, the2000Chinahas entered the aging society. How to provide for the aged has become a major problemfor the society. Learn from the basic experience of pension reform of developedcountries facing population aging, in order to solve the shortage conditions undertraditional old-age insurance, our country shall have to bring forth new ideas to thepension insurance system. To accumulate living cost after retirement through annuity isone of them. As the traditional fixed annuity’s payment in the settlement period is fixed,not adjust with inflation, at the same time the risk is assumed entirely by the policyholder, it can no longer meet people’s needs. An equity indexed annuity (Hereinafterreferred to as EIA) linked to a certain equity index has been quickly developed.EIA can guarantee the principal as well as the investment income from loss, and atthe same time, on the basis of minimum income guarantee, its equity is related to theperformance of a certain pre-specified stock or bond index. As EIA has a minimumincome guarantee, the policy holders can not be100%involved in the growth of thestock index, but in a certain ratio, this ratio is the participation rate. In the past study onEIA, it is often tend to be risk-free interest rate. So, to a large extent can not value theEIA in real life accurately. In this paper, bases on the study of Serena Tiong, weconsider the pricing of EIA under stochastic interest rate, provide the pricing formula ofEIA under the simple point-to point method and the annual re-try method, and conduct anumerical simulation to analyze the factors that influence the participation rate.The framework of this thesis is as follows: The first part mainly introduces thebackground of Equity Index Annuity and what EIA is. The second part introduces someterminologies and basic tools this paper needs. Part three, the Martingale PricingMethod is used to price EIA with dividend under stochastic interest rate, and provide theformula of EIA under simple point-to point method and the annual re-try method. Thelast part, sensitivity analysis, a numerical simulation is conducted to analyze the factors that influence the participation rate.