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題名：死亡風險的自然避險與商品設計
作者：黃芳文 引用關係
校院名稱：國立政治大學
系所名稱：風險管理與保險研究所
指導教授：蔡政憲
學位類別：博士
出版日期：2015
主題關鍵詞：死亡風險；長壽風險；自然避險；mortality risk；longevity risk；natural hedging
原始連結：連回原系統網址new window
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對必須維持長期清償能力的壽險公司來說，如何做好死亡率的風險管理是極為基本的。過去的文獻上提出，利用保險公司銷售的壽險商品(如：終身壽險)，因具有死亡風險，對具有長壽風險的商品(如：年金險)可產生避險效果。這種商品組合的自然避險方式是顯而易見的，但可能因為僵化的銷售市場與誘因導向的銷售方式等因素，商品組合的自然避險是較為難以執行的。我們提出的是，把自然避險策略植入商品設計中，可以把避險效果內含於商品內容裡面。關鍵在於讓這張保單在死亡事件發生的時間點所產生的影響可以被抵銷，我們技巧性地選取給付成長參數，即“應給付多少”因子，可以決定死亡給付的金額現值，而利率因子δ洽可反映給付的時間價值。本論文集提供壽險商品與年金商品的理論推導、圖解說明以及數值分析，一一闡述我們的想法以及如何將自然避險融入於商品設計之中。
在第一篇中，我們利用精算的方法推導，得到利用壽險商品設計範疇內可以達到最佳化化的自然避險策略。在第二篇的論文中，依據第一篇自然避險策略的理論基礎下的商品設計，我們除更進一步探討在死亡率與利率條件不確定的因素下，對於以最佳化避險策略的商品，可產生的影響，我們以實際的數據分析，得到即使對於未來的死亡率與利率不確定的情況下，我們所提出的依理論條件下的最佳化避險策略所設計的商品，仍能使商品所產生的死亡率風險極小化，甚至接近於無死亡率風險。除以壽險商品為主要設計外，在第三篇論文中，我們也呈現以年金商品為架構的商品設計。
How to manage mortality rate risks is essential to the long-term solvency of life insurance companies. The literatures proposed to hedge the products subject to the longevity risk (such as annuities) by using the products subject to the mortality risk (e.g., whole life insurance) sold by an insurer. Such natural hedging is intuitive but may be difficult to implement due to the rigid sales market and incentive issues. We propose to embed natural hedging into product design so that the hedging may occur within a product. The key is to offset the impact of mortality on the timing of death that in turn determines the present value of the death benefit by cleverly choose the growth rate of the death benefit, the factor of “how much to pay” while δ would reflect the time value of payment. This article provides theoretical derivations, graphical illustrations, and numerical analyses of both life insurance products and annuity products to illustrate the idea of embedding natural hedging into product design.
In the first essay, we use actuarial methods to come up with the theoretical derivation of the optimal natural hedging strategy and we can easily embed it into insurance product design. In the second essay, furthermore, we evaluate the impact of uncertainty passed on by future mortality rate and interest rate against the product design based on the optimal natural hedging strategy. We use the numerical illustration and obtain the minimum risk or nearly no risk at all under the optimal strategy. We develop not only on the life insurance product design, in the third essay, we also progress the product design of annuity products.
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