二十一世紀以來，隨著科技醫療技術日益精進，死亡率疾速下降，全球人口平均壽命逐年提高，使壽險公司面臨龐大的長壽風險，如何解決長壽風險等相關議題，已成當前壽險公司主要目標之一。為了有效降低長壽風險（longevity risk） 的影響，壽險公司常利用金融市場將長壽風險進行證券化，發展為長壽風險衍生性商品。此保險型金融商品標的指數與經由死亡率指數調整的存活率指數所連動，屬於死亡率證券化的延伸商品，如何準確地預測未來死亡率為定價關鍵。
本文將預測死亡率模型以及評價方式分開討論，使用Lee-Carter model搭配extreme value theorem（極值理論）以及bootstrap（拔靴法）兩項預估死亡率模型預測出未來死亡率，再分別搭配Wang transform valuation和canonical valuation兩項評價方式，針對歐洲投資銀行（European Investment Bank）發行EIB/BNP longevity bond（2004）計算其公平價格（fair value）與風險溢酬，提供後續對長壽商品定價之研究參考。
本文的主要貢獻為：(1)依據英國歷史資料，採用Lee-Carter model搭配極值理論以及拔靴法刻劃死亡率的未來路徑與分配。(2)採用Wang transform valuation和canonical valuation針對長壽債券進行計算，並計算出隱含風險溢酬，用以判斷價格的合理性。

The advancement of technology and medical treatment technique leads to the decline of mortality rapidly and the increase of life expectancy of population over the years. Therefore, life insurance companies face a huge longevity risk as issuing relevant insurance contracts. In order to reduce longevity risk, life insurance companies usually use longevity risk securitization in the financial markets, and transform it into longevity risk derivatives. The purpose of securitization is to transfer longevity risk. The underlying index of the insurance-linked securities is associated with the survival index, which is made up and adjusted by the mortality model. Longevity bonds are also classified as mortality-linked derivatives. As a result, to accurately predict future mortality has been pivotal to price those securities.
This article discusses the mortality forecast and bond valuation. First we uses Lee-Carter model with extreme value theorem and bootstrap method to forecast future mortality. Second we apply Wang transform valuation and Canonical valuation to calculate the fair value as well as risk premium of the EIB/BNP longevity bond（2004）issued by European Investment Bank respectively. It could be a reference for the following study of pricing longevity bond.
This paper mainly has two contributions：First of all, on the basis of historical data, we adopt the Lee-Carter model with extreme value theorem and bootstrap method to simulate the future mortality paths and distributions. Second, we calculated the implied market risk premium of longevity bond to evaluate the rationality of longevity bond pricing.

壹、緒論
一、研究目的
二、研究方法
三、研究架構
貳、文獻回顧
第一節 風險證券化
第二節 死亡率預測模型
一、死亡率模型簡介
二、Lee-Carter model
三、Bootstrap method （拔靴法）
第三節 長壽債券定價方法
一、Wang transform valuation
二、Canonical valuation
參、死亡率預估模型與債券評價方法
第一節 死亡率預估模型
一、原始Lee-carter model
二、極值理論Extreme Value theory （EVT）
三、Lee-Carter Model with EVT
四、Bootstrap method
第二節 債券評價方法
一、Wang transform
二、Canonical valuation
肆、實證結果
第一節 長壽債券簡介及資料來源
一、歐洲投資銀行長壽債券簡介 – The EIB/BNP longevity bond
二、資料來源
第二節 死亡率預估結果
一、Lee-Carter EVT
二、拔靴法
第三節 長壽債券評價結果
一、債券定價方式與假設
二、長壽債券定價結果
三、風險溢酬
伍、結論
參考文獻
附錄一：不完備市場定價法
附錄二：瑞士再保死亡率債券簡介 – The Swiss Re VitaⅠmortality bond

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