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    Title: 附有最低保證給付投資型保險之評價與分析
    Authors: 曾柏方
    Tseng, Po-fang
    Contributors: 廖四郎
    呂桔誠


    曾柏方
    Tseng, Po-fang
    Keywords: 附有最低保證給付投資型保險
    HJM模型
    平賭訂價理論
    equity-linked Life insurance policies with and asset value guarantee
    HJM model
    Martingale
    Date: 2003
    Issue Date: 2009-09-14 09:27:00 (UTC+8)
    Abstract: 有鑑於附有最低保證給付投資型保險期末現金流量與選擇權如出一轍，是以應用平賭訂價理論(The Martingale Pricing Method)嵌入HJM利率模型，對隨機利率下附有最低保證給付投資型保險進行評價。並對繳費方式與利率型態兩議題所構成四種類型附有最低保證給付投資型保險作實地數據模擬與評價，以及敏感度分析。
    研究結果可以歸納為四點結論。
    (1) 單就附有最低保證給付投資型保險簡化版（忽略期中死亡理賠與期滿生存機率）而言：
    可視為是最低保證給付折現與以之為履約價的買權組合。因此，當影響因子僅與買權有相關性時，附有最低保證給付投資型保險與理論買權的敏感度分析結果，如出一轍。連動標的期初價格與波動度變動於附有最低保證給付投資型保險影響便是實證。
    (2) 延續上點論述衍生：
    當影響因子同時對買權與附有最低保證給付折現具有相關性時，由於買權佔整個保險價值比重過低，是以主要影響力皆來自附有最低保證給付的變動。附有最低保證給付與固定利率折現因子變動對於保險價值影響，即反應此結果。
    (3) 分別就繳費方式不同下，投保年齡與投保期限變動對於附有最低保證給付投資保險的影響而言：
    躉繳型繳費方式下，由第二點結論可得，投保期限越長保費越低，是以當投保年齡越大，期中死亡率提高，且期間短的保費較高的情況下，投保年齡變動對於附有最低保證給付投資型保險影響為正向；分期繳型繳費方式下，由於條款設定不同，無法與躉繳型一概而論，反映在投保期間越長保單價值與保費皆增加，但若是比較其增加的幅度（二階條件小於零）逐漸減少，倒是與躉繳型投資保險投保期間與保費關係意思相同，只是呈現方式不同。分期繳型投資型保險保單價值與投保年齡關係，從投保期限與保費關係以及高年齡層死亡率較高，可以得知，隨著投保年齡的增加，分期繳型投資保險中因為死亡理賠的現金流量產生機會提高，而此部分期間短保單價值較低，是以投保年齡與保單價值呈現反比關係，但是保單價值平準化後的保費，源於平準因子每期存活率因投保年齡增加而減少，造成投保年齡越高，保費也越高。
    (4) 就性別而言：
    躉繳型附有最低保證給付投資保險，由於女性相較於男性死亡率較低，容易取得期間較長的期滿保證金，而此部分價值較低，是以女生保費較男生便宜；分期繳型附有最低保證給付投資保險，則是相反的表現，由於此部分價值較高，是以女性的保險價值高於男性，同時因女性平準因子中的存活率也比男性高，是以每期所要繳交的保費也比男性低廉。
    (5) 就利率型態而言：
    隨機利率下躉繳型投資型保險與固定利率下躉繳型投資保險相較，便宜許多，主要是因為利率型態為隨機，且期初利率期間結構打破水平狀態的假設，真實反應正常期初利率期間結構(Normal Interest Rate Term Structure)，是以評價出的保費較固定利率型態下的保費低廉，甚至於分期繳型附有最低保證給付投資保險，在隨機利率下，隨著投保期限增加，保費反而下降。
    Reference: 1. 中文部分
    (1) 中華民國人壽保險商業同業公會(2003)，台灣壽險業第四回經驗生命表，初版，台北市：中華民國人壽保險商業同業公會。
    (2) 林鴻鈞(2003)，「六大重點看保本商品：如何說明投資型保單是最佳選擇」，Advisers財務顧問，第175期，115-117。
    (3) 張智星(2000)，MATLAB程式設計與應用，初版，新竹市：清蔚科技。
    (4) 張斐然(2003)，投資型保單入門學習地圖，初版，台北市：早安財經文化。
    (5) 陳松男(2002)，金融工程學：金融商品創新選擇權理論，初版，台北市：華泰。
    (6) 陳威光(2001)，選擇權：理論、實務與應用，初版，台北市：智勝。
    (7) 廖泗滄(1988)，壽險數理，初版，台北市：台北市人壽保險商業同業公會。
    (8) 鄭榮治(1999)，壽險數理要義—精算師入門基石，第二版，台北市：華泰。譯自Life Insurance Primary Mathematics.
    2. 英文部分
    (1) Black, F. and M.J. Scholes (1973), “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, 81, 637-659.
    (2) Black, F., E.Derman and W. Toy (1990), “A One-Factor Model of Interest Rates and Its Applications to Treasury Bond Options.” Financial Analysts Journal, Jan-Feb, 33-39.
    (3) Bolye, P. (1977), “A Monte Carlo Approach.” Journal of Financial Economics, 4, 323-338.
    (4) Brennan, M. J., and E.S. Schwartz (1976),”The Pricing of Equity-Linked
    Life Insurance Policies with an Asset Value Guarantee.” Journal of
    Financial Economics, 3, 195-213.
    (5) Carverhill, A. and L. Clewlow (1990), “Flexible Convolution.” Risk, 3, 25-29.
    (6) Cerny, A. (2003), Mathematical Techniques in Finance: Tools for Incomplete Markets, 1st ed., U.S.A., Princeton and Oxford.
    (7) Clewlow, L. and C. Strickland (1998), Implementing Derivatives Models, 1st ed., England, John Wiley & Sons Ltd.
    (8) Cox, J. C., J. E. Ingersoll, S. A. Ross (1985), “A Theory of the Term Structure of Interest Rates.” Econometrica, Vol. 53, No 2,385-408.
    (9) Gerber, H.U. and E.S. Shiu (1994), “Option Pricing by Esscher Transforms.” Transactions of the Society of Actuaries, 46, 99-140.
    (10) Hardy, M.R. (2000), “Hedging and Reserving for Single-Premium Segregated Fund Contracts.” North American Actuarial Journal, Vol. 4, No. 2, 63-74.
    (11) Health, D., R. Jarrow, and A. Morton (1992), “Bond Pricing and the Term structure of Interest Rates: A New Methodology for Contingent Claims Valuation.” Econometrica, Vol. 60, No 1, 77-105.
    (12) Ho, T., and S. Lee (1986),”Term Structure Movements and Pricing Interest Rates Contingent Claims.” Journal of Finance, 41, 1011-1029.
    (13) Hull, J., and A. White (1994), “Numerical Procedure for Implementing Term Structure Models Ⅱ: Two Factor Models.” The Journal of Derivatives, Vol. 2, 37-49.
    (14) Hull, J.C. (2000), Options, Futures& Other Derivatives, 4th ed., U.S.A.
    , Prentice-hall International.
    (15) Lee, H. (2003),” Pricing Equity-Indexed Annuities with Path-Dependent Options.” Insurances: Mathematics and Economics, 33, 677-690.
    (16) Mψller, T.(1998), “Hedging Equity-Linked Life Insurance Contracts.” North American Actuarial Journal, Vol. 5, No. 2, 79-95.
    (17) Neftci, S. N. (2000), An Introduction to the Mathematics of financial Derivatives, 2nd ed., U.S.A., Academic Press.
    (18) Nielsen, J.A., K. Sandmann(1995), ” Equity-Linked Life Insurance: a Model with Stochastic Interest Rates.” Insurances: Mathematics and Economics, 16, 225-253.
    (19) Nonnenmacher, D.J.F., J. Ruβ (1998), “Arithmetic Averaging Equity-Linked Life Insurance Policies in Germany.” Insurances: Mathematics and Economics, 25, 23-35.
    (20) Persson, S. A., K. K. Aase (1997), “Valuation of the Minimum Guaranteed Return Embedded in Life Insurance Products.” The Journal of Risk and Insurance, Vol.64, No. 4, 599-617.
    (21) Porter, M. E. (1985), Competitive Advantage: Creating and Sustaining Superior Performance, New York: Free Press; London: Collier Macmillan.
    (22) Tiong, S. (1998), “Valuing Equity-Linked Annuities.” North American Actuarial Journal, Vol. 4, No. 4, 149-170.
    (23) Turnbull, S. M. and L. M. Wakeman (1991), “Quick algorithm for Pricing European Average Options.” Journal of Financial and Quantitative Analysis, 77-389.
    (24) Vasciek, O. (1977), “An Equilibrium Characterization of the Term Structure.” Journal of Financial Economics, 5, 177-188.
    (25) Vorst, A. C. F. (1992),”Pricing and Hedge Ratios of Average Exchange Rate Options” International Review of Financial Analysis, 1,179-193.
    (26) Windcliff, H., P.A. Forsyth, K.R. Vetzal (2001), “Valuation of Segregated Funds: Shout Options with Maturity Extensions.” Insurances: Mathematics and Economics, 29, 1-21.
    (27) ZAgst, R. (2002), Interest-Rate Management, 1st ed., Germany, Springer.
    Description: 碩士
    國立政治大學
    金融研究所
    91352017
    92
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0091352017
    Data Type: thesis
    Appears in Collections:[Department of Money and Banking] Theses

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