在保險商品市場裡，附保證權益連結年金保險日趨流行，這樣的投資型保險不僅提供投保人參與投資連結的指數，並且在保單到期時，擁有最低保證收益，讓投保人在市場蓬勃時，可以獲得較高的報酬；但在市場低迷時，仍保有最低收益。然而，在過去的文獻當中，大部分的附保證權益連結年金保險訂價，都假設在Black and Scholes 選擇權訂價模型下做評價，但其假設標的資產波動度為常數並不符合真實情況，因此，本文使用Heston and Nandi (2003) 所提出的GARCH 模型，放寬標的資產波動度為常數的假設，並將其與Hsieh and Chiu (2007) 中每年重設法 (Ratchet) 下的附保證權益連結年金保險訂價結合，並且採用標準普爾500指數 (S&P 500 index) 做為連結指數，探討在隨機波動度的假設下與資產波動度為常數的假設下，附保證權益連結年金保險訂價的差異。本文實證結果顯示，在GARCH 模型下的附保證權益連結年金保險價格較資產波動度為常數的假設下的價格高，表示在Black and Scholes 選擇權訂價模型下的價格低估。將附保證權益連結年金保險的評價模式與隨機波動度模型結合，不但可使商品評價過程更接近真實情況，並且合適的運用在理論與實務的銜接。ABSTRACT 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.
