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題名 權益連結壽險之動態避險：風險極小化策略與應用
Dynamic Hedging for Unit-linked Life Insurance Policies: Risk Minimization Strategy and Applications作者 陳奕求
Chen, Yi-Chiu貢獻者 張士傑<br>陳威光
Chang, Shih-Chieh<br>Chen, Wei-Kuang
陳奕求
Chen, Yi-Chiu關鍵詞 等價原則
Black-Scholes評價公式
不完全市場
均數變異避險
風險極小化
principal of equivalience
Black-Scholes valuation formula
markets incompleteness
mean-variance hedging
risk-minimization
self-finance strategy
counting process
intrinsic risk日期 2001 上傳時間 18-Apr-2016 16:28:46 (UTC+8) 摘要 傳統人壽保險契約之分析利用等價原則(principal of equivalience) 來對商品評價。即保險人所收保費之現值等於保險人未來責任(保險金額給付)之現值。然而對於權益連結壽險商品而言，其結合傳統商品之風險(如利率風險、死亡率風險等)與財務風險，故更增加其評價困難性。過去研究中在假設預定利率為常數與死亡率為給定的情況下，利用Black-Scholes (1973)評價公式推導出公式解。然而Black-Scholes評價公式是建構在完全市場上，對於權益連結壽險商品而言其已不符合完全市場之假設，因此本文放寬完全市場之假設來對此商品重新評價與避險。
In this study, actuarial equivalent principle and no-arbitrage pricing theory are used in pricing and valuation for unit-linked life insurance policies. Since their market values cannot be replicated through the self-finance strategies due to market incompleteness, the theoretical setup in Black and Scholes (1973) and Follmer and Sondermann (1986) are adopted to develop the pricing and hedging strategies. Counting process is employed to characterize the transition pattern of the policyholder and the linked assets are modeled through the geometric Brownian motions. Equivalent martingale measures are adapted to derive the pricing formulas. Since the benefit payments depend on the performance of the underlying portfolios and the health status of the policyholder, mean-variance minimization criterion is employed to evaluate the financial risk. Finally pricing and hedging issues are examined through the numerical illustrations. Monte Carlo method is implemented to approximate the market premiums according to the payoff structures of the policies. In this paper, we show that the risk-minimization criterion can be used to determine the hedging strategies and access the minimal intrinsic risks for the insurers.參考文獻 一、中文部分1.陳松男與鄭翔伊(1999), 「組合型權證之正確評價即避險方法」證券市場發展季刊 第十一卷第四期。2.郭怡馨，「保本型變額壽險之評價分析」，國立政治大學風險管理與保險學研究所碩士論文，民國88年6月。二、英文部分1.Aase, K.K and Person , S.A.(1994).”Pricing of Unit-Linked Life Insurance Policies,” Scandivnal Actuarial Journal 1:26-52.2.Bacinello, A.R. and F. Ortu(1993b).”Pricing equity-linked life insurance with endogenous minimum guarantees,” Insurance Mathematics and Economics 12, 245-252.3.Bacinello, A.R. and Persson, S.A.(1998).”Design and Pricing of Equity-Linked Life Insurance under Stochastic Interest Rate , ” Preprint, Institute of Finance and Management Science. The Norwegian School of Economics and Business Administration.4.Black. F. and Scholes. M.(1973).”The pricing of options and corporate liabilities, ” Journal of Political Economy 81:637-654.5.Bjork, T.(1996). Arbitrage Theory in Continuous Time, Stockholm School of Econnmics.6.Brennan, M.J. and Schwartz, E.S.(1976).”The Pricing of Equity-Linked Life Insurance Policies with an Asset Value Guarantee,” Journal of Financial Economics 3:195-213.7.Brennan, M.J. and Schwartz, E.S. (1979a).”Alternative Investment Strategies for the Issuers of Equity-Linked Life Insurance Policies with an Asset Value Guarantee,” Journal of Business 52:63-93.8.Brennan, M.J. and Schwartz, E.S. (1979b). ”Pricing and Investment Strategies for Guaranteed Equity-Linked Life Insurance,” Monograph no. 7 The S. S. Huebner Foundation for Insurance Education, Wharton School, University of Pennsylvania, Philadelphia.9.Broadie, M and Detemple, J. (1995) “Amercian Capped Call Options on Dividend-Paying Assets, ” The Review of Fiancial Studies 8:161-191.10.Follmer, H and D. Sondermann (1986). “Hedging of non-redundant Contingent Claims,” Contributions to Mathematical Economics, 205-223.11.Follmer, H and M. Schweizer (1988). “Hedging by sequential regression: An introduction to the mathematics of option trading,” The ASTIN Bulletin 18(2):147-160.12.Gentle, D (1993). “Basket weaving, ” Risk (6), 51-52.13.Harrison, J. M. and Pliska, S. R. (1981). “Martingales and Stochastic Integrals in the Theory of Continuous Trading, ” Stochastic Process and their Applications 11, 215-260.14.Hull, John C. (2000). Options, Futures, and Other Derivatives, Fourth edition.15.Johnson, Herb (1987). “Options on the Maximum or the Minimum of Several Assets, ” Journal of Financial and Quantitative Analysis 22, 277-282.16.Margrabe, W. (1978). “The Value of an Option to Exchange One Asset for Another, ” Journal of Finance 33, 177-186.17.Moller, T (1996). “Risk-Minimizing Strategies for Unit-Linked Life Insurance Products, ” Master Thesis.18.Moller, T (1998a). “Risk-Minimizing Hedging Strategies for Unit-Linked Life Insurance Contracts, ” ASTIN Bulletin 28, 17-47.19.Moller, T (2000). “Quadratic Hedging Approaches and Indifference Pricing in Insurance, ” Ph.D. Thesis.20.Nielsen, J. and K. Sandmann (1995). “Equity-linked Life Insurance：A Model with Stochastic Interest Rates,” Insurance Mathematics and Economics 16, 225-253.21.Samuel, H. Turner. (1971). Equity-based Life Insurance in the United Kingdom.22.Schal, M.(1994), “On Quadratic Cost Criteria for Option Hedging, ” Mathematics of Operation Research 19, 121-131.23.Schweizer, M. (1988), “Hedging of Options in a General Semimartingale Model, ” Diss. ETHZ NO 8615, Swiss Federal Institute of Technology, Zurich.24.Schweizer, M. (1991), “Option Hedging for Semimartingale, ” Stochastic Processes and their Application 37, 339-363.25.Schweizer, M. (1993), “Approximating Random Variables by Stochastic Integrals, and Applications in Financial Mathematics, ” Habiltationsschrift, University of Gottingen.26.Schweizer, M. (1994), “Risk-Minimizing Hedging Strategies under Restricted Information, ” Mathematical Finance 4, 327-342.27.Schweizer, M. (1995a), “Variance-Optimal Hedging in Discrete Time, ” Mathematics of Operation Research 20, 1-32.28.Schweizer, M. (1995b), “Approximation Pricing and the Variance-Optimal Martingale Measure, ” to appear on Annals of Probability.29.Stulz, R. (1982) “Options on the Minimum or the Maximum of Two Risky Asset：Analysis and Applications, ” Journal of Financial Economics 10, 161-185. 描述 碩士
國立政治大學
風險管理與保險研究所
88358015資料來源 http://thesis.lib.nccu.edu.tw/record/#A2002001470 資料類型 thesis dc.contributor.advisor 張士傑<br>陳威光 zh_TW dc.contributor.advisor Chang, Shih-Chieh<br>Chen, Wei-Kuang en_US dc.contributor.author (Authors) 陳奕求 zh_TW dc.contributor.author (Authors) Chen, Yi-Chiu en_US dc.creator (作者) 陳奕求 zh_TW dc.creator (作者) Chen, Yi-Chiu en_US dc.date (日期) 2001 en_US dc.date.accessioned 18-Apr-2016 16:28:46 (UTC+8) - dc.date.available 18-Apr-2016 16:28:46 (UTC+8) - dc.date.issued (上傳時間) 18-Apr-2016 16:28:46 (UTC+8) - dc.identifier (Other Identifiers) A2002001470 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/85419 - 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) 88358015 zh_TW dc.description.abstract (摘要) 傳統人壽保險契約之分析利用等價原則(principal of equivalience) 來對商品評價。即保險人所收保費之現值等於保險人未來責任(保險金額給付)之現值。然而對於權益連結壽險商品而言，其結合傳統商品之風險(如利率風險、死亡率風險等)與財務風險，故更增加其評價困難性。過去研究中在假設預定利率為常數與死亡率為給定的情況下，利用Black-Scholes (1973)評價公式推導出公式解。然而Black-Scholes評價公式是建構在完全市場上，對於權益連結壽險商品而言其已不符合完全市場之假設，因此本文放寬完全市場之假設來對此商品重新評價與避險。 zh_TW dc.description.abstract (摘要) In this study, actuarial equivalent principle and no-arbitrage pricing theory are used in pricing and valuation for unit-linked life insurance policies. Since their market values cannot be replicated through the self-finance strategies due to market incompleteness, the theoretical setup in Black and Scholes (1973) and Follmer and Sondermann (1986) are adopted to develop the pricing and hedging strategies. Counting process is employed to characterize the transition pattern of the policyholder and the linked assets are modeled through the geometric Brownian motions. Equivalent martingale measures are adapted to derive the pricing formulas. Since the benefit payments depend on the performance of the underlying portfolios and the health status of the policyholder, mean-variance minimization criterion is employed to evaluate the financial risk. Finally pricing and hedging issues are examined through the numerical illustrations. Monte Carlo method is implemented to approximate the market premiums according to the payoff structures of the policies. In this paper, we show that the risk-minimization criterion can be used to determine the hedging strategies and access the minimal intrinsic risks for the insurers. en_US dc.description.tableofcontents 封面頁證明書致謝詞論文摘要目錄圖目錄表目錄第一章 緒論1.1 研究背景1.2 研究動機與目的1.3 研究範圍與步驟1.4 研究架構第二章 相關文獻回顧及理論探討2.1 財務與精算評價之結合2.2 『權益連結壽險商品』之回顧與檢視2.3 『風險極小化策略』理論第三章 避險理論與模型3.1 不完全市場之評價與避險3.2 風險極小化避險策略3.3 舉例說明: 權益連結生存保險3.4 新奇權益連結壽險之避險與風險第四章 個案模擬分析4.1 模擬分析4.2 附有最低保證之生存保險4.3 具有兩種風險資產組合之生存保險4.4 模擬結果比較分析第五章 結論與後續研究建議5.1 結論5.2 後續研究與建議參考文獻附錄附錄A 符號表 zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#A2002001470 en_US dc.subject (關鍵詞) 等價原則 zh_TW dc.subject (關鍵詞) Black-Scholes評價公式 zh_TW dc.subject (關鍵詞) 不完全市場 zh_TW dc.subject (關鍵詞) 均數變異避險 zh_TW dc.subject (關鍵詞) 風險極小化 zh_TW dc.subject (關鍵詞) principal of equivalience en_US dc.subject (關鍵詞) Black-Scholes valuation formula en_US dc.subject (關鍵詞) markets incompleteness en_US dc.subject (關鍵詞) mean-variance hedging en_US dc.subject (關鍵詞) risk-minimization en_US dc.subject (關鍵詞) self-finance strategy en_US dc.subject (關鍵詞) counting process en_US dc.subject (關鍵詞) intrinsic risk en_US dc.title (題名) 權益連結壽險之動態避險：風險極小化策略與應用 zh_TW dc.title (題名) Dynamic Hedging for Unit-linked Life Insurance Policies: Risk Minimization Strategy and Applications en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) 一、中文部分1.陳松男與鄭翔伊(1999), 「組合型權證之正確評價即避險方法」證券市場發展季刊 第十一卷第四期。2.郭怡馨，「保本型變額壽險之評價分析」，國立政治大學風險管理與保險學研究所碩士論文，民國88年6月。二、英文部分1.Aase, K.K and Person , S.A.(1994).”Pricing of Unit-Linked Life Insurance Policies,” Scandivnal Actuarial Journal 1:26-52.2.Bacinello, A.R. and F. Ortu(1993b).”Pricing equity-linked life insurance with endogenous minimum guarantees,” Insurance Mathematics and Economics 12, 245-252.3.Bacinello, A.R. and Persson, S.A.(1998).”Design and Pricing of Equity-Linked Life Insurance under Stochastic Interest Rate , ” Preprint, Institute of Finance and Management Science. The Norwegian School of Economics and Business Administration.4.Black. F. and Scholes. M.(1973).”The pricing of options and corporate liabilities, ” Journal of Political Economy 81:637-654.5.Bjork, T.(1996). Arbitrage Theory in Continuous Time, Stockholm School of Econnmics.6.Brennan, M.J. and Schwartz, E.S.(1976).”The Pricing of Equity-Linked Life Insurance Policies with an Asset Value Guarantee,” Journal of Financial Economics 3:195-213.7.Brennan, M.J. and Schwartz, E.S. (1979a).”Alternative Investment Strategies for the Issuers of Equity-Linked Life Insurance Policies with an Asset Value Guarantee,” Journal of Business 52:63-93.8.Brennan, M.J. and Schwartz, E.S. (1979b). ”Pricing and Investment Strategies for Guaranteed Equity-Linked Life Insurance,” Monograph no. 7 The S. S. Huebner Foundation for Insurance Education, Wharton School, University of Pennsylvania, Philadelphia.9.Broadie, M and Detemple, J. (1995) “Amercian Capped Call Options on Dividend-Paying Assets, ” The Review of Fiancial Studies 8:161-191.10.Follmer, H and D. Sondermann (1986). “Hedging of non-redundant Contingent Claims,” Contributions to Mathematical Economics, 205-223.11.Follmer, H and M. Schweizer (1988). “Hedging by sequential regression: An introduction to the mathematics of option trading,” The ASTIN Bulletin 18(2):147-160.12.Gentle, D (1993). “Basket weaving, ” Risk (6), 51-52.13.Harrison, J. M. and Pliska, S. R. (1981). “Martingales and Stochastic Integrals in the Theory of Continuous Trading, ” Stochastic Process and their Applications 11, 215-260.14.Hull, John C. (2000). Options, Futures, and Other Derivatives, Fourth edition.15.Johnson, Herb (1987). “Options on the Maximum or the Minimum of Several Assets, ” Journal of Financial and Quantitative Analysis 22, 277-282.16.Margrabe, W. (1978). “The Value of an Option to Exchange One Asset for Another, ” Journal of Finance 33, 177-186.17.Moller, T (1996). “Risk-Minimizing Strategies for Unit-Linked Life Insurance Products, ” Master Thesis.18.Moller, T (1998a). “Risk-Minimizing Hedging Strategies for Unit-Linked Life Insurance Contracts, ” ASTIN Bulletin 28, 17-47.19.Moller, T (2000). “Quadratic Hedging Approaches and Indifference Pricing in Insurance, ” Ph.D. Thesis.20.Nielsen, J. and K. Sandmann (1995). “Equity-linked Life Insurance：A Model with Stochastic Interest Rates,” Insurance Mathematics and Economics 16, 225-253.21.Samuel, H. Turner. (1971). Equity-based Life Insurance in the United Kingdom.22.Schal, M.(1994), “On Quadratic Cost Criteria for Option Hedging, ” Mathematics of Operation Research 19, 121-131.23.Schweizer, M. (1988), “Hedging of Options in a General Semimartingale Model, ” Diss. ETHZ NO 8615, Swiss Federal Institute of Technology, Zurich.24.Schweizer, M. (1991), “Option Hedging for Semimartingale, ” Stochastic Processes and their Application 37, 339-363.25.Schweizer, M. (1993), “Approximating Random Variables by Stochastic Integrals, and Applications in Financial Mathematics, ” Habiltationsschrift, University of Gottingen.26.Schweizer, M. (1994), “Risk-Minimizing Hedging Strategies under Restricted Information, ” Mathematical Finance 4, 327-342.27.Schweizer, M. (1995a), “Variance-Optimal Hedging in Discrete Time, ” Mathematics of Operation Research 20, 1-32.28.Schweizer, M. (1995b), “Approximation Pricing and the Variance-Optimal Martingale Measure, ” to appear on Annals of Probability.29.Stulz, R. (1982) “Options on the Minimum or the Maximum of Two Risky Asset：Analysis and Applications, ” Journal of Financial Economics 10, 161-185. zh_TW
