臺灣博碩士論文加值系統

摘要
權益指數年金是一種遞延年金，具有最低保證給付與股價指數相連結的特色。由於有最低報酬的保證，權益指數年金的報酬通常無法百分之一百參與股價指數上漲的報酬。年金持有人應獲得多高的參與率才是合理？或保險公司應訂多少的參與率才能符合最低保證費用的需要？基於權益指數年金為長期契約，考量利率為隨機變動是有其必要性的。因此，本論文運用Amin and Jarrow（1992）隨機利率選擇權評價模型，研究在簡單點對點利率計算機制下，權益指數年金之合理參與率。情境分析結果顯示，當最低保證利率愈低、上限愈低、到期日愈長、股票報酬率之總波動幅度愈小、利率波動函數中之一固定參數愈小、遠期利率和股票報酬率之負相關係數愈大、利率波動函數中之另一參數愈大時，參與率則愈高。另外，當利率期限結構分別呈現上升、水平及下降的趨勢時，參與率則會呈現隨之增加、趨於定值及隨之減少的狀態。最後，與固定利率下所模擬出參與率之差異作一分析比較：當固定利率之股價波動度與隨機利率之股票報酬率總波動幅度為一致，且固定利率與債券收益率亦為同一值時，到期日愈長，隨機利率下所模擬出之參與率均會小於固定利率下所模擬出之參與率值；其中，又僅以利率波動函數中之一固定參數愈大且到期日愈長及股票報酬率之總波動幅度愈小時，與固定利率下參與率之差距亦會愈大。所以，當權益指數年金之期間愈長或利率波動函數中之一固定參數相對股票報酬率之總波動幅度愈大時，將動態隨機利率的影響納入考量是一項相當重要的課題。

Abstract
Most of the equity indexed annuities (EIAs) have the following main features: a guaranteed minimum, a formula for determining and crediting interest in excess of the guaranteed minimum, the linkage of an equity index performance, and all the usual components of a fixed deferred annuity. There exist many different interest-crediting formulas being used. The issue of how to design the fair crediting structure will be examined under the Heath-Jarrow-Morton (1992) stochastic interest rate dynamic. The fairness is, in a sense, consistent with no-arbitrage conditions in the financial markets. In this paper, the fair crediting structure of the simple point-to-point crediting method is determined by using Amin and Jarrow’s (1992) stochastic interest rate option-pricing formula. Employing the closed-form options pricing formula, it can be shown that the parameters of a fair crediting structure must be set to satisfy some equation. The results of scenario analysis show that the increase of forward rate volatility reduces the participation rate. Furthermore, the longer the term of the EIA, the larger the reduction impact.

第一章 緒論………………………………….………………………1
第一節 研究背景、動機與目的……………………………………1
第二節 研究方法與限制………………………………….…. ….4
第三節 論文架構…………………………………………………..4
第二章 文獻回顧…………………………………………………….5
第一節 隨機利率之文獻探討………………………………………5
第二節 隨機利率下之選擇權評價…………………………………6
第三節 權益指數年金之參與率文獻探討…………………………9
第三章 權益指數年金之選擇權評價模型…………………………10
第一節 權益指數年金之財務架構……………………………….10
第二節 權益指數年金之評價－Black-Scholes模型之應用……11
第三節 權益指數年金之評價－Amin-Jarrow模型之應用………12
第四章 模型之情境分析（Scenario Analysis）與結果……….16
第一節 參與率與其他相關參數之變化關係…………………….18
第二節 參與率在不同利率期限結構下之變化………………….24
第三節 隨機利率與固定利率之參與率比較…………………….25
第五章 結論與建議…………………………………………………27
參考文獻………………………………………………………………29
表目錄
表4-1 相關參數之數值........16
附表4-1 點對點之參與率模擬....32
附表4-2 點對點之參與率模擬....32
附表4-3 點對點之參與率模擬....33
附表4-4 點對點之參與率模擬....33
附表4-5 點對點之參與率模擬....34
附表4-6 點對點之參與率模擬....34
附表4-7 點對點之參與率模擬....35
附表4-8 點對點之參與率模擬....35
附表4-9 點對點之參與率模擬....36
附表4-10 點對點之參與率模擬....36
附表4-11 點對點之參與率模擬....37
附表4-12 點對點之參與率模擬....37
附表4-13 點對點之參與率模擬....38
附表4-14 點對點之參與率模擬....38
附表4-15 點對點之參與率模擬....39
附表4-16 點對點之參與率模擬....39
附表4-17 點對點之參與率模擬....40
附表4-18 點對點之參與率模擬....40
圖目錄
圖4-1 最低保證利率對參與率之影響……………………………………...18
圖4-2 上限對參與率之影響…………………………………….…………..19
圖4-3 到期日對參與率之影響…………………………………….………..20
圖4-4 股票報酬率之總波動幅度對參與率之影響………………………...22
圖4-5 利率波動函數中之一固定參數對參與率之影響…………………...22
圖4-6 遠期利率和股票報酬率之負相關係數對參與率之影響……….…..23
圖4-7 利率波動函數中之另一參數對參與率之影響……….……………..23
圖4-8 不同利率期限結構之參與率分析……………………….…………..24
圖4-9 隨機利率與固定利率之參與率比較（一）………………….………25
圖4-10 隨機利率與固定利率之參與率比較（二）………………….………26
圖4-11 隨機利率與固定利率之參與率比較（三）………………….………26

參考文獻
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