TheGood-deal PricingModelfor the Equity-linked Life Insurance

投資型保單評價：優勢交易定價法之應用

10.6545/JFS.2008.16(1).6

羅烈明(Lieh-Ming Luo)；許和鈞(Her-Jiun Sheu)；胡毓彬(Yu-Pin Hu)

投資型保單 ； 無套利價格 ； 優勢交易定價法 ； Equity-linked Life Insurance ； No-arbitrage Price ； Good-deal Pricing Approach

財務金融學刊

16卷1期（2008 / 03 / 31）

159 - 182

英文

本研究以Cochrane與Saa-Requejo（2000）所提出的優勢交易定價法（Good-deal Pricing Approach）應用於投資型保單之評價，並與最早由Brennan與Schwartz（1976）所發展的傳統投資型係單評價方法進行比較。傳統的評價方法假設死亡率與資產價格隨機過程相互獨立，以及保險人對死亡率具風險中立性，本研究藉結合資產價格隨機過程與被保險人死亡隨機過程，建立一個新的隨機過程，以放寬此二項基本假設，並將投資型保單視為該新的隨機過程下的一項或有請求權。由於該新的隨機過程屬於不完備市場，故保單的無套利價格非唯一，本研究應用前述之優勢交易定價法估算投資型保單之合理價格，並說明在特定的條件下，傳統評價方法是優勢交易定價法的一個特例。此外，本文亦證明當死亡率與資產價格隨機過程相互獨立時，傳統方法與優勢交易定價法含有相同的評價結果。最後輔以數值分析，說明在死亡率與資產價格隨機過程並非相互獨立的情況下，優勢交易定價法如何產生與傳統方法不同的評價結果，數值結果亦顯示優勢交易定價法所產生的合理價格具特殊的經濟意涵。

The good-deal pricing approach by Cochrane and Saa-Requejo (2000) is adopted for the valuation of the equity-linked life insurance product in this paper. This topic was studied by using the conventional approach, as proposed by Brennan and Schwartz (1976) and other researchers before, The basic idea behind the good-deal pricing approach is that any product design of the equity-linked life insurance could be viewed as contingent claims of a new underlying discrete process combining the price process of a reference fund and the death process of an insured. Since the new underlying process set is referred to an incomplete market, the no-arbitrage price of the contract would constitute bounds rather than give a specified value. The good-deal asset pricing approach is applied for this incomplete market case. The fair price we found is different from the result of the conventional approach. It is verified that the conventional approach result could be derived as a special case of the good-deal approach. Finally, numerical analyses are conducted to illustrate the comparative properties of the two pricing approaches. According to the numerical results, the fair price by the good-deal approach would yield the reasonable economic implication, which is consistent with the proposed relationship embodied in the consumption-based pricing approach.

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