死亡率改善與總體因子之領先效果在死亡率模型建構之研究

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姓名

李哲緯(Che-Wei Li) 查詢紙本館藏

畢業系所

財務金融學系

論文名稱

死亡率改善與總體因子之領先效果在死亡率模型建構之研究
(A Study of Mortality Improvement and Macroeconomic Leading Lags in Mortality Modeling)

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摘要(中)

隨著科技日新月異，人口有更好的醫療資源，壽命也逐漸延長，各個國家皆有相同趨勢，透過良好的動態模型預測死亡率有助於減少錯誤訂價之機率。Milidonis and Efthymiou (2015)研究亞太地區之死亡率改善發現經濟發展較好的國家對經濟發展較差之國家具有領先關係，且驗證存在短期的預測能力。本研究以Lee-Carter (LC)模型 (Lee and Carter, 1992)為架構，延伸考慮其他影響死亡率改善之總體因子，透過向量自我相關 (Vector Autoregression；VAR)方法對LC模型的預測方法修正，並以台灣人口死亡率以及總體因子來配適，透過Improvement ratio驗證模型之改進有助於提升預測之準確度。最後，應用於近期較熱門之附保證投資型商品─保證終生最低提領給付商品 (Guaranteed Life-time Withdrawal Benefits; GLWB)，並透過敏感度分析參數與商品之影響程度。

摘要(英)

With the advancement of technology, the population have better medical resources. Life is also gradually extended. Every country have the same trend. Through good dynamic model to predict mortality helps reduce the probability of mispricing. Milidonis and Efthymiou (2015) found that mortality risk improvements flow from more developed to less developed countries. And there exists a short-term predictability. In this research, I use the Lee-Carter model (Lee and Carter, 1992) which is one of the most popular model in the related research. This study extends the consideration of other economic factors associated with mortality improvement. Through vector autoregression (VAR) method to modify the LC model. We show that the modified models help to improvement the accuracy of predictability by using the data of Taiwan. Finally, we apply a popular product recently which is the Guaranteed Life-time Withdrawal Benefits (GLWB). And use sensitivity analysis to see impact between parameters and product.

關鍵字(中)

★ 長壽風險
★ Lee-Carter模型
★ 死亡率預測
★ 向量自我迴歸
★ 附保證投資型商品

關鍵字(英)

★ Longevity Risk
★ Lee-Carter Model
★ Mortality Forecasting
★ Vector Autoregression (VAR)
★ Guaranteed Investment-Oriented Insurance Product

論文目次

第一章緒論 1
1.1 前言 1
1.2 研究目的 3
第二章死亡率模型建構的文獻 5
第三章模型與方法 7
3.1 Lee-Carter死亡率模型建構 7
3.2 Lee-Carter死亡率模型之參數估計 9
3.3 Vector Autoregression (VAR) 11
3.3.1 單根檢定 11
3.3.2 VAR模型及落後期數 13
3.3.3 Granger因果檢驗 14
3.4 Forecasting and Fitting 15
3.4.1 修正LC預測死亡率模型 15
3.4.2 樣本內配適衡量標準 15
第四章實證結果 16
4.1 台灣六都之Vector Autoregression (VAR) 16
4.1.1 台灣六都之單根檢定 16
4.1.2 台灣六都之VAR模型及落後期數 17
4.1.3 台灣六都之Granger因果檢驗 17
4.2 台灣六都之Forecasting and Fitting 23
4.2.1 台灣六都之死亡率模型預測 23
4.2.2 台灣六都之In-Sample Fitting 24
第五章應用─保證終生最低提領給付 26
5.1 附保證投資型商品 26
5.1.1 附保證商品介紹 26
5.1.2 附保證提領投資型商品文獻探討 27
5.2 資產動態假設 28
5.3 帳戶動態假設 29
5.4 GLWB之Payoffs 29
5.5 數值結果與敏感度分析 31
5.5.1 數值精算 31
5.5.2 敏感度分析 33
第六章結論 36
參考文獻 38
附錄一 42
附錄二 43
附錄三 48
附錄四 50
附錄五 51

參考文獻

國內參考文獻
1. 劉議謙 2008，附保證提領保險商品之評價，東吳大學商用數學系碩士論文
2. 郭維裕、李淯靖、林楚彬 2012，保險死亡率期限結構之共同因子分析與配適，行政院國家科學委員會專題研究計畫

國外參考文獻
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17. Liu, Y. 2010. Pricing and Hedging the Guaranteed Minimum Withdrawal Benefits in Variable Annuities.
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指導教授

楊曉文

審核日期

2015-7-8

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