臺灣博碩士論文加值系統

投資型商品連動於特定資產，保險人除了面臨原有的核保風險，更需承擔部分的財務風險。傳統保險商品的純保費價格等於其預期損失，而投資型商品的保險給付依據投資標的波動，保險人的預期損失不易估算，傳統精算的評價方法不完全適用於投資型商品。保證最低給付的給付結構使得投資型商品具有選擇權的特質，Brennan與Schwartz (1976)首先利用選擇權定價理論探討附有保證最低給付投資型商品之價值與避險策略，爾後亦有許多文獻以此方向加以著墨，但選擇權定價理論是基於市場為完全市場的假設，保險市場為不完全市場，以完全市場假設之理論評定保險商品之價值實不合理。本為假設保險人面臨的風險為核保風險及財務風險，財務市場為完全市場，保險人可以藉由市場上的各種金融商品建構避險組合規避財務風險；而預期死亡人數與實際死亡人數所產生的核保誤差，保險人無法利用避險組合完全地規避，因此保險市場為不完全市場。
在不完全市場中請求權的價值牽涉投資者主觀的風險偏好，不存在唯一的平賭測度，請求權的價格也不唯一，最適避險策略依請求權的價格調整，所以投資型保險商品的價格不再等於其公平價值，真正的成交價格應落於買賣價差之中。本文引用Mercurio (1996)的結果，利用二次效用函數，以極大化保險人期末財富之效用為目標，建構生存險的合理價格範圍。以二元樹模型描述股票的波動，分別模擬五年、十年及十五年投資型生存險之價差範圍，保險人的風險規避程度、保單期限以及保證金額的高低將影響商品價差範圍的大小。

Investment-linked life (LIL) insurance policies integrate the attributes from the mutual fund by introducing the investment options to the policyholders and life insurance through the benefit payments shielding the unexpected events of the insured. Since the execution of the implied options depends on the policyholder’s health status. Actuarial equivalent principal and non-arbitrage pricing theory are used in evaluating the prices for LIL insurance policies. Brennan and Schwartz (1976) initially employ the option pricing theory in examining the pricing and hedging strategy for LIL insurance policies with minimum guarantees. Most published literatures are focusing on this issue adopting the B-S methodology. Since the values of the LIL policies cannot be replicated uniquely through the self-financing strategies due to underwriting risks of the insurance market. Insurance market does not satisfy the completeness assumptions,
Due to lack of a unique martingale measure under market incompleteness, the utility assumption of the policyholder is involved in the pricing issue. Insurance pricing must consider the risk attitude of the investors in the market. Hence the cost the LIL insurance policies are not necessarily equal to the fair market prices. The market value should fall within the range of the bid and ask prices. In this study, we follow the approach in Mercurio (1996) by adopting the quadratic utility function and compute the reasonable range of the prices based on maximizing the terminal health utility function. Binary tree method is used in modeling the asset dynamics. Then the numerical computations are performed using endowment LIL insurance policies with 5, 10 and 15 years of duration. Based on the results, we find that the risk attitude of the policyholder, the policy duration and minimum amounts of the guarantees significantly affect the bid-ask price spread of LIL insurance policies.

第一章 緒論…………………………………………………1
1.1 研究背景與動機……………………………………….1
1.2 研究範圍與目的……………………………………….4
1.3 研究架構………………………………………………6
第二章 文獻回顧……………………………………………8
2.1 美國標準評價準則之相關規定…………………………8
2.2 忽略核保風險之評價問題……………………………..10
2.2.1 投資型商品與保證成本之評價………………….10
2.2.2 新奇選擇權之評價……………………………...12
2.3 考慮核保風險之評價問題……………………………..13
2.4 不完全市場之評價問題………………………………..17
2.5 效用函數對於評價之影響……………………………..20
第三章 投資型商品之定價與避險策略…………………...24
3.1 財務理論與核保計數過程……………………………..29
3.1.1 財務理論……………………………………….29
3.1.2 核保計數過程…………………………………..31
3.2 風險偏好與均變異數評價準則………………………...33
3.3 投資型商品的公平避險價格與避險策略……………….42
第四章 個案模擬分析……………………………………...46
4.1節 投資型商品與情境之假設…………………………..46
4.2節 核保誤差之估算……………………………………48
4.3節 模擬結果分析………………………………………49
第五章 結論與後續研究…………………………………...55
參考文獻…………………………………………………...…59

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陳奕求，「權益連結壽險之動態避險：風險極小化策略與應用」，國立政治大學風險管理與保險學研究所碩士論文，民國90年6月。
陳雅正，「論投資型保險之監理」，國立政治大學風險管理與保險學研究所碩士論文，民國90年6月。