Analytic Approximation Formulae for Minimum Rate of Return Guarantees under Garch

考慮GARCH效果之最低保證收益分析近似解

林忠機(Chung-Gee Lin)；謝長杰(Chang-Chieh Hsieh)；王珣(Shun Wang)

析近似 ； Edgeworth展開 ； 保證 ； analytical approximation ； edgeworth expansion ； GARCH ； guarantee

中國統計學報

52卷3期（2014 / 09 / 01）

300 - 334

英文

具有最低收益保證之股權連結人壽保險保單, 在目前的壽險產業已經是一項受到民眾歡迎的金融工具。然而，即便連結的標的資產具有GARCH的特性，但是過去卻沒有研究針對GARCH下的最低收益保證商品進行評價與避險分析。本研究整合Edgeworth擴充技術，進一步推導出考慮GARCH效果之最低保證收益商品的分析近似解。根據數值分析的結果，當以大樣本模擬法為標竿值，本研究的分析近似解表現非常優秀。本研究的模型可提供保險從業人員一個評估GARCH下最低保證收益商品非常實用的評價與避險工具。

Equity-linked life insurance policies with a minimum rate of return guarantee (ELI MG) have become popular instruments in the insurance service industry. However, despite the presence of an inherent GARCH (generalized autoregressive conditional heteroskedasticity) feature in linked financial underlying, no studies address the pricing and hedging of ELIMG under GARCH. This research extends previous research by integrating the Edgeworth expansion for deriving analytical approximation formulae of ELIMG with GARCH. According to numerical experiments, the analytical approximation solution performs very well compared with large sample Monte Carlo simulations. The analytical approximation solution is easy to implement for pricing and hedging ELIMG under GARCH and thus provides a practical tool for the insurance practitioners.

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