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題名 解約率因素下附保證給付投資型保險的風險價差
Risk bearing spreads of GMMB with lapse rates dependent on economic factors作者 潘冠宇 貢獻者 張士傑
潘冠宇關鍵詞 風險價差
滿期給付投資型保險
經濟因子脫退率
risk spreads
GMMB
lapse rates日期 2011 上傳時間 30-Oct-2012 11:24:42 (UTC+8) 摘要 近年來因市場波動劇烈, 保險公司紛紛推出的「附保證投資型保單」, 給予保戶在投資上的保證。然而, 附最低給付保證條件卻使得保險公司必須面對更大的核保與財務風險。所以計算出附有最低保證條件商品的保費就顯得格外地重要。 傳統附保證保單在訂價時,都是假設固定己知的脫退率,因為他們認為脫退率的變化不會是影響保單價值的主因。但在Mary hardy 所著的《Investment Guarantees》一書中page 96 特別提到脫退風險:Withdrawals are more problematic. Withdrawals are, to someextent, related to the investment experience, and the withdrawal risk is, therefore, not fully diversifiable.因此, 本文希望透過建立受經濟因子影響的解約率模型,來得到附保證保險的風險價差。 本文考慮附保證滿期給付投資型商品(GMMB),並且使用 Heston (1993)提出的財務市場模型以及參考Mercurio (1996,2001) 評價投資型保險之風險承擔價差方法, 使用效用函數來描述保險契約雙方之風險趨避程度。同時根據Kolkiewicz & Tan (2006) 假設受經濟因子的危險比率模型(hazardrate model), 來反映出資產的平均波動程度會影響保戶的脫退率。最後以情境方式分別模擬5、10及15年到期的附保證最低滿期投資型保險之風險價差。本研究推導之模型主要得出下列結果: (1) 保單期間愈長, 價差愈大。(2) 價外賣權的價差高於價內。(3) 風險規避程度越高買賣價差越大。(4) 脫退率受經濟影響愈深, 保單的買賣價差愈大。(5) 當保險公司所保證的價格愈高時, 價差的影響愈大。
With the fluctuation in the financial market in 2008, insurance company provided the consumers with equity-linked life insurances embedded guarantees. On the other hand, there are more risk in the financial literacy and underwriting performance of the insurance company. It is especially important to calculate the premium of the contract embedded investment guarantee properly .Traditional method of pricing the contract embedded investment guarantee was assumed that lapse rate was known, because product providers believed lapse rate was not a major factor to price the contract. However,Mary hardy’s ”Investment Guarantees” page 96 specifically mentions about the lapse rate risk:Withdrawls are more problematic. Withdrawals are, to someextent ,related to the investment experience, and the withdrawal risk is, therefore, not fully diversifiable.So this article will found the model of lapse rate dependent on economic factors and further get the fair value of one kind of a contract embedded guarantee: GMMB.We will build a financial model introduced by Heston (1993) and use the methodology provided by Mercurio (1996,2001) to price the risk bearing gap of a contract embedded guarantee with utility function to depict the risk averse level between investors . And we have lapse rates affected fromthe fluctuation of the implying asset which is the hazard rate model used by Kolkiewicz & Tan (2006). Finally, we will simulate a set of scenarios to present the Risk bearing spreads of equity-linked life insurance embeddedguarantees whose term are 5、10 and 15 years. The following are the consequences I got: (1) The longer the duration, the larger the spread. (2) The spread out of money is larger than that in the money. (3) The higher the risk aversion, the larger the buy-ask spread. (4) The deeper the influenceof economy on the lapse rate, the larger the buy-ask spread. (5) The higher guarantee price insurer offer, the deeper the spread affect.參考文獻 張士傑著, 保險契約之評價與風險管理, 前程文化事業有限公司, 民國99年6月。林忠機、楊曉文著, 附保證給付投資型保險之定價與風險評估, 保險事業發展中心, 民國100年10月。Brennan, M. J., & Schwartz, E. S. (1976). The pricing of equity-linked life insurance policies with an asset value guarantee. Journal of Financial Economics, 3(3), 195-213.Chang, M. C., & Jiang, S.-j. (2010). Surrender effects on policy reserves:a simulation analysis of investment guarantee contracts. Global Journal of Business Research, Vol. 4, No. 4, pp. 11-21, 2010.Chris O’Brien (2006) The downfall of equitable life in the United Kingdom:the mismatch of strategy and risk management, Risk Management and Insurance Review, volume9, issue 22,189-204.Coleman, T. F., Levchenkov, D., & Li, Y. (2007). Discrete hedging of American-type options using local risk minimization. Journal of Banking & Finance, 31(11).F¨ollmer, H., & Schweizer, M. (1988). Hedging by sequential regression: An introduction to the mathematics of option trading. ASTIN Bulletin, 18(2), 147-160.F¨ollmer, H., & Sondermann, D. (1985). Hedging of non-redundant contingent claims. [Discussion Paper Serie B].Hardy, M. (2003). Investment guarantees: modeling and risk management for equity-linked life insurance: John Wiley & Sons.Kim, C. (2005). Modeling surrender and lapse rates with economic variables.North American Actuarial Journal, 9(4), 56-70.Kolkiewicz, A. W., & Tan, K. S. (2006). Unit-linked life insurance contracts with lapse rates dependent on economic factors. Annals of Actuarial Science, 1, 49-78.Møller, T. (1998). Risk-minimizing hedging strategies for unit-linked life insurance contracts. ASTIN Bulletin, 28(1), 17-47.Mercurio, F. (2001). Claim pricing and hedging under market incompleteness and ”mean-variance” preferences. European Journal of Operational Research, 133(3), 635-652.Sch¨al, M. (1994). On quadratic cost criteria for option hedging. Mathematics of Operations Research, 19(1), 121-131.Schweizer, M. (1988). Hedging of options in a general semimartingale mode.[Ph.D. dissertation].Schweizer, M. (1991). Option hedging for semimartingales. Stochastic Processes and their Applications, 37, 339-363.Schweizer, M. (1994a). Risk-minimizing medging strategies under restricted information. Mathematical Finance, 4, 327-342.Schweizer, M. (1995b). On theMinimalMartingaleMeasure and the F¨ollmer-Schweizer Decomposition. Stochastic Analysis and Applications, 13, 573-599.Schweizer, M., & F¨ollmer, H. (1988). Hedging by Sequential Regression:an Introduction to the Mathematics of Option Trading. ASTIN Bulletin,18(2), 147-160.32 描述 碩士
國立政治大學
風險管理與保險研究所
99358023
100資料來源 http://thesis.lib.nccu.edu.tw/record/#G0099358023 資料類型 thesis dc.contributor.advisor 張士傑 zh_TW dc.contributor.author (Authors) 潘冠宇 zh_TW dc.creator (作者) 潘冠宇 zh_TW dc.date (日期) 2011 en_US dc.date.accessioned 30-Oct-2012 11:24:42 (UTC+8) - dc.date.available 30-Oct-2012 11:24:42 (UTC+8) - dc.date.issued (上傳時間) 30-Oct-2012 11:24:42 (UTC+8) - dc.identifier (Other Identifiers) G0099358023 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/54601 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 風險管理與保險研究所 zh_TW dc.description (描述) 99358023 zh_TW dc.description (描述) 100 zh_TW dc.description.abstract (摘要) 近年來因市場波動劇烈, 保險公司紛紛推出的「附保證投資型保單」, 給予保戶在投資上的保證。然而, 附最低給付保證條件卻使得保險公司必須面對更大的核保與財務風險。所以計算出附有最低保證條件商品的保費就顯得格外地重要。 傳統附保證保單在訂價時,都是假設固定己知的脫退率,因為他們認為脫退率的變化不會是影響保單價值的主因。但在Mary hardy 所著的《Investment Guarantees》一書中page 96 特別提到脫退風險:Withdrawals are more problematic. Withdrawals are, to someextent, related to the investment experience, and the withdrawal risk is, therefore, not fully diversifiable.因此, 本文希望透過建立受經濟因子影響的解約率模型,來得到附保證保險的風險價差。 本文考慮附保證滿期給付投資型商品(GMMB),並且使用 Heston (1993)提出的財務市場模型以及參考Mercurio (1996,2001) 評價投資型保險之風險承擔價差方法, 使用效用函數來描述保險契約雙方之風險趨避程度。同時根據Kolkiewicz & Tan (2006) 假設受經濟因子的危險比率模型(hazardrate model), 來反映出資產的平均波動程度會影響保戶的脫退率。最後以情境方式分別模擬5、10及15年到期的附保證最低滿期投資型保險之風險價差。本研究推導之模型主要得出下列結果: (1) 保單期間愈長, 價差愈大。(2) 價外賣權的價差高於價內。(3) 風險規避程度越高買賣價差越大。(4) 脫退率受經濟影響愈深, 保單的買賣價差愈大。(5) 當保險公司所保證的價格愈高時, 價差的影響愈大。 zh_TW dc.description.abstract (摘要) With the fluctuation in the financial market in 2008, insurance company provided the consumers with equity-linked life insurances embedded guarantees. On the other hand, there are more risk in the financial literacy and underwriting performance of the insurance company. It is especially important to calculate the premium of the contract embedded investment guarantee properly .Traditional method of pricing the contract embedded investment guarantee was assumed that lapse rate was known, because product providers believed lapse rate was not a major factor to price the contract. However,Mary hardy’s ”Investment Guarantees” page 96 specifically mentions about the lapse rate risk:Withdrawls are more problematic. Withdrawals are, to someextent ,related to the investment experience, and the withdrawal risk is, therefore, not fully diversifiable.So this article will found the model of lapse rate dependent on economic factors and further get the fair value of one kind of a contract embedded guarantee: GMMB.We will build a financial model introduced by Heston (1993) and use the methodology provided by Mercurio (1996,2001) to price the risk bearing gap of a contract embedded guarantee with utility function to depict the risk averse level between investors . And we have lapse rates affected fromthe fluctuation of the implying asset which is the hazard rate model used by Kolkiewicz & Tan (2006). Finally, we will simulate a set of scenarios to present the Risk bearing spreads of equity-linked life insurance embeddedguarantees whose term are 5、10 and 15 years. The following are the consequences I got: (1) The longer the duration, the larger the spread. (2) The spread out of money is larger than that in the money. (3) The higher the risk aversion, the larger the buy-ask spread. (4) The deeper the influenceof economy on the lapse rate, the larger the buy-ask spread. (5) The higher guarantee price insurer offer, the deeper the spread affect. en_US dc.description.tableofcontents 1 緒論. . . . . . . . . . . . . . . . .. . . . . . . . . .11.1 研究目的與動機. . . . . . . . . . . . . . . . . . . . . 11.2 研究架構. . . . . . . . . . . . . . . . . . . . . . . . 32 商品介紹與文獻回顧. . . . . . . . . . . . . . . . . . . . .42.1 附保證投資型商品介紹. . . . . . . . . . . . . . . . . . . 42.2 台灣市售附保證投資商品. . . . . . . . . . . . . . . . . . 62.3 文獻回顧. . . . . . . . . . . . . . . . . . . . . . . . 83 模型建立. . . . . . . . . .. . . . . . . . . . . . . .103.1 保證最低滿期金額保險(GMMB) 現金流. . . . . . . . . . . . 103.2 財務市場模型. . . . . . . . . . . . . . . . . . . . . . 133.3 脫退率模型. . . . . . . . . . . . . . . . . . . . . . 153.4 偏好均變異數準則. . . . . . . . . . . . . . . . . . . . 174 研究結果 . .. . . . . . . . . . . . . . . . .. . . . . . 204.1 投資型商品與情境假設 .. . . . . . . . . . . . . . . . . 204.2 數值呈現與整理. . . . . . . . . . . . . . . . . . . . . 245 分析與結論. . . . . . . . . .. . . . . . . . . . . . . .29參考文獻. . . . . . . . . ...... . . . . . . . . . . . . .31 zh_TW dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0099358023 en_US dc.subject (關鍵詞) 風險價差 zh_TW dc.subject (關鍵詞) 滿期給付投資型保險 zh_TW dc.subject (關鍵詞) 經濟因子脫退率 zh_TW dc.subject (關鍵詞) risk spreads en_US dc.subject (關鍵詞) GMMB en_US dc.subject (關鍵詞) lapse rates en_US dc.title (題名) 解約率因素下附保證給付投資型保險的風險價差 zh_TW dc.title (題名) Risk bearing spreads of GMMB with lapse rates dependent on economic factors en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) 張士傑著, 保險契約之評價與風險管理, 前程文化事業有限公司, 民國99年6月。林忠機、楊曉文著, 附保證給付投資型保險之定價與風險評估, 保險事業發展中心, 民國100年10月。Brennan, M. J., & Schwartz, E. S. (1976). The pricing of equity-linked life insurance policies with an asset value guarantee. Journal of Financial Economics, 3(3), 195-213.Chang, M. C., & Jiang, S.-j. (2010). Surrender effects on policy reserves:a simulation analysis of investment guarantee contracts. Global Journal of Business Research, Vol. 4, No. 4, pp. 11-21, 2010.Chris O’Brien (2006) The downfall of equitable life in the United Kingdom:the mismatch of strategy and risk management, Risk Management and Insurance Review, volume9, issue 22,189-204.Coleman, T. F., Levchenkov, D., & Li, Y. (2007). Discrete hedging of American-type options using local risk minimization. Journal of Banking & Finance, 31(11).F¨ollmer, H., & Schweizer, M. (1988). Hedging by sequential regression: An introduction to the mathematics of option trading. ASTIN Bulletin, 18(2), 147-160.F¨ollmer, H., & Sondermann, D. (1985). Hedging of non-redundant contingent claims. [Discussion Paper Serie B].Hardy, M. (2003). Investment guarantees: modeling and risk management for equity-linked life insurance: John Wiley & Sons.Kim, C. (2005). Modeling surrender and lapse rates with economic variables.North American Actuarial Journal, 9(4), 56-70.Kolkiewicz, A. W., & Tan, K. S. (2006). Unit-linked life insurance contracts with lapse rates dependent on economic factors. Annals of Actuarial Science, 1, 49-78.Møller, T. (1998). Risk-minimizing hedging strategies for unit-linked life insurance contracts. ASTIN Bulletin, 28(1), 17-47.Mercurio, F. (2001). Claim pricing and hedging under market incompleteness and ”mean-variance” preferences. European Journal of Operational Research, 133(3), 635-652.Sch¨al, M. (1994). On quadratic cost criteria for option hedging. Mathematics of Operations Research, 19(1), 121-131.Schweizer, M. (1988). Hedging of options in a general semimartingale mode.[Ph.D. dissertation].Schweizer, M. (1991). Option hedging for semimartingales. Stochastic Processes and their Applications, 37, 339-363.Schweizer, M. (1994a). Risk-minimizing medging strategies under restricted information. Mathematical Finance, 4, 327-342.Schweizer, M. (1995b). On theMinimalMartingaleMeasure and the F¨ollmer-Schweizer Decomposition. Stochastic Analysis and Applications, 13, 573-599.Schweizer, M., & F¨ollmer, H. (1988). Hedging by Sequential Regression:an Introduction to the Mathematics of Option Trading. ASTIN Bulletin,18(2), 147-160.32 zh_TW
