台灣人口近幾年老化問題益趨嚴重，在亞洲僅次於日本，並且於1993年正式進入聯合國所界定的高齡化社會，如何有效管理高齡化問題已成為各國所重視的議題。在風險管理上，以純粹連結死亡率的死亡率債券(mortality bond)及長壽債券(longevity bond)逐漸受到重視。文獻上針對死亡率連結商品做定價的方式有很多種，為規避其他訂價方式可能產生的模型風險及參數風險，本文嘗試以canonical valuation approach搭配無母數方法預估死亡率對longevity bond進行定價。本研究亦將結果與Wang transform定價結果做比較，希望可以提供長壽債券一個更好的定價方式。

In recent years, the problem of aging in Taiwan's population is getting worse, which is second only to Japan in Asia. Besides, Taiwan is officially defined as the aging society by the United Nations in 1993. The method of how to effectively manage the aging problem has become a national issue. In risk management, people have gradually paid their attention to both the mortality bonds and the longevity bonds which are purely linked to mortality rate. There are many ways to price mortality-linked instruments in literatures. In order to circumvent the model risk and the parameter risk which arise from the other methods, we attempts to use the canonical valuation approach with nonparametric method to forecast mortality rate for pricing longevity bonds. The results of this study will be also compared to the pricing of Wang transform, and we hope that this study may provide a better pricing method for longevity bonds.

壹、緒論 1
貳、文獻回顧 3
一、死亡率連結債券商品簡介 3
二、死亡率連結債券模型簡介 6
參、死亡率預測模型與評價方法 9
一、Canonical Valuation of Mortality-Linked Securities 9
二、 Canonical Valuation基本概念 10
三、年齡和時間的數據相依性 11
四、拔靴數值方法 14
五、死亡率預估 15
六、存活率預估 18
七、求解Canonical Measure 19
肆、債券定價及數值結果 24
一、資料來源 24
二、長壽債券定價 24
三、求解Wang transform評價方法下的風險市場價格(λ_t) 28
伍、結論及建議 30
一、結論 30
二、研究限制及建議 31
陸、附錄 32

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