臺灣博碩士論文加值系統

本文主要針對匯率連動權益指數年金（Quanto Equity-Indexed Annuities）做評價，首先，先介紹三種不同權益指數年金（Equity-Indexed Annuities，EIA），分別為點對點（Point-to-Point）、高水檔（High Water Mark）和年度重設（Annual Ratchet），而年度重設又可分為複利年度重設（Compound Annual Ratchet）和簡單年度重設（Simple Annual Ratchet）。接著，我們介紹了單資產Quanto模型和多資產Quanto模型，並推導出單資產Quanto EIA的封閉解。由於多資產Quanto EIA無封閉解，本研究運用蒙地卡羅法來評價商品價格，並利用變異數縮減方法，使其模擬速度增快。我們使用了控制變異法（Control Variates）和反向變異法（Antithetic Variates），發現兩者同時使用的變異數縮減效果最佳。最後，本文透過調整參與率、上限率、下限率、利率和匯率與連結標的的相關係數來觀察成本的變化，提供建議予商品發行商。

第一章 緒論 6
第一節 研究動機 6
第二節 研究目的 9
第二章 文獻探討 10
第一節 EIA商品介紹 10
ㄧ、 單資產連結 10
二、 多資產連結 13
第二節 蒙地卡羅模擬法介紹 14
ㄧ、 反向變異法（Antithetic Variates） 17
二、 控制變異法（Control Variates） 17
第三章 研究方法與模型設定 20
第一節 單資產Quanto模型 20
第二節 多資產Quanto模型 24
第四章 數值例子 27
第一節 單資產Quanto EIA 27
第二節 多資產Quanto EIA 32
第五章 結論 73

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