An equity-indexed annuity (EIA) with maturity guarantee is getting more popular in insurance companies. It provides policyholders not just participate the investment in linked index, but still have the minimum guarantee payoff at the maturity of contract. However, most of litera-ture is pricing the EIA contract under the Black and Scholes assumptions that the assets prices follow the geometric Brownian motion, and the volatility is constant. Under the assumptions, the valuation of EIA may result in some pricing error, and the pricing procedure will be more inaccurate and unrealistic. Therefore, in this paper, we broaden the constant volatility assump-tion and introduce the volatility model that is the GARCH process in Heston and Nandi (2003) into valuation. We do the valuation in two type of ratchet EIA, compound and simple, and let S&P 500 index as the linked index. We use the analytic pricing formulas in Hsieh and Chiu (2007) to get the prices under the Black and Scholes assumptions. Moreover, numerical analy¬sis also shows the prices of two types of ratchet EIAs with maturity guarantee in constant volatil¬ity and under GARCH process. The results show that under the GARCH process, the prices of EIA are higher than the prices under con¬stant volatility which means the prices un¬der Black and Scholes assumptions are underestimated. Combining the volatility model into EIA valuation makes the pricing process more practical. It is much closer to the real¬ity situa¬tion and useful in actual products valuation.
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