本文主要比較用主成份分析與波動度建構出來的指數在連結固定指數年金上是否會比單純連結大盤的報酬來的優越，並利用Heston Nandi GARCH 模型去模擬波動度，計算固定指數年金的參與率，讓保險公司在成本控管與避險時，不會受保戶選擇固定利率或連結指數報酬上有太大影響。結果顯示固定指數年金連結主成份建構出來的指數，能比連結大盤或波動度建構出來的指數累積報酬更好。且在給定信賴水準下，主成份建構指數的條件尾端期望風險相對於波動度建構出來的指數是較小的。證實多因子配置在2011年至2018年間比僅用單一因子波動度建構來的有效。

The purpose of this study is to investigate whether the multi-factor index may perform better than the simple volatility-weighted index. The Heston Nandi GARCH model is adopted to simulate the volatility, and then calculate the participation rate of Fixed index(ed) annuities(FIAs). The insurance company can utilize the participation rate to control the cost and hedge the risk for FIAs. The results show that the index conducted by the Principal component analysis (PCA) perform better than market weight index and volatility weight index. In addition, the conditional tail expectations of the index conducted by PCA are smaller than other two indices given the confidence interval, which shows that factor index is more efficient than volatility index and market weight index.

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