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題名 隨機利率下可解約利率變動型壽險評價分析
The Valuation Analysis of Floating-rate Life Insurance under Stochastic Interest Rates作者 林靜吟
Lin, Ching-Yin貢獻者 林士貴<br>蔡政憲
Lin, Shih Kuei<br>Tsai, Cheng-Hsien
林靜吟
Lin, Ching-Yin關鍵詞 條件期望值
利變型保單
Hull and white
Conditional expectation
CRR
Floating-rate insurance policy日期 2018 上傳時間 3-Jul-2018 17:26:44 (UTC+8) 摘要 本文在Hull and White隨機利率模型之下計算利率變動型壽險的公平保費及其隱含之解約選擇權。本文提出遞迴公式並逆向計算保單價值，應用條件期望值的方法，建構二維樹狀結構計算利變型壽險的保費。利用本文提出的二維樹狀結構評價，不但具有精確性與收斂特性，計算上也十分有效率。本文也同時分析影響公平保費與解約選擇權價值之各項因子，包含利率波動度，資產波動度，利率和資產相關係數等。分析指出當利率波動劇烈時，利率變動型壽險價值與解約選擇權價值會隨著增加；區隔資產帳戶價值波動度劇烈時，利率變動型壽險價值會隨著減少而解約選擇權價值會隨著增加；最後，利率和區隔資產帳戶價值相關係數越高，利率變動型壽險價值越低，而解約選擇權價值越高。本文提出之評價方法與數值分析結果可供於保險公司評價利率變動型商品之參考。
This paper provides the fair valuation of a floating-rate life insurance policy embedded with surrender options under Hull and White stochastic interest rate models. This paper proposes a recursive formula to implement the backward computation and a two dimensions tree structure is constructed by the Conditional Expectation method to value the fair premiums of floating-rate life insurance policy. By using the proposed algorithm, we analyze the factors affecting the value of premiums and surrender options. Numerical analysis indicates that high interest rate volatility enhances both the premiums and surrender options values entitled to the policyholder. Moreover, when the value of segregate asset account has a high degree of volatility, the premiums of floating-rate life insurance will decrease and the value of surrender options will increase. Finally, the higher the correlation coefficient between the interest rate and the value of segregate asset account, the lower the premiums of floating-rate life insurance, conversely, the higher the value of the surrender options. These results present some suggestions for insurance companies to issue a floating-rate life insurance contract embedded with surrender options.參考文獻 一、 中文文獻 [1] 李明黛. (2002). 利率風險對公司經營之影響:台灣壽險市場之實證研究. 政治大學風險管理與保險學系碩士學位論文. [2] 林士貴, 張智凱, & 廖四郎. (2008). 可解約分紅保單之遞迴評價公式. 財務金融學刊, 16(3), 107-147. [3] 賴詩婷. (2011). 隨機利率模型下分紅保單之解約選擇權評價. 逢甲大學統計與精算學系碩士學位論文. [4] 王禕鴻. (2015). 利率變動型壽險探討. 中央大學財務金融學系碩士在職專班學位論文. 二、 英文文獻 [1] Bacinello, A. R., & Ortu, F. (1993). Pricing equity-linked life insurance with endogenous minimum guarantees. Insurance: Mathematics and Economics, 12(3), 245-257. [2] Bacinello, A. R. (2001). Fair pricing of life insurance participating policies with a minimum interest rate guaranteed. ASTIN Bulletin: The Journal of the IAA, 31(2), 275-297. [3] Bacinello, A. R. (2003a). Fair valuation of a guaranteed life insurance participating contract embedding a surrender option. Journal of Risk and Insurance, 70(3), 461-487. [4] Bacinello, A. R. (2003b). Pricing guaranteed life insurance participating policies with annual premiums and surrender option. North American Actuarial Journal, 7(3), 1-17. [5] Bacinello, A. R. (2005). Endogenous model of surrender conditions in equity-linked life insurance. Insurance: Mathematics and Economics, 37(2), 270-296. [6] Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637-654. [7] Briys, E., & De Varenne, F. (1997). On the risk of insurance liabilities: debunking some common pitfalls. Journal of Risk and Insurance, 673-694. [8] Cox, J. C., Ingersoll Jr, J. E., & Ross, S. A. (2005). A theory of the term structure of interest rates. In Theory of Valuation, 129-164. [9] Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7(3), 229-263. [10] Hao, J. C. (2011). The pricing for interest sensitive products of life insurance firms. Scientific Research, 2, 194-202. [11] Hilliard, J., A. Schwartz, and A. Tucker (1996). Bivariate binomial options pricing with generalized interest rate processes. The Journal of Financial Research, 19, 585-602. [12] Ho, T. S., Stapleton, R. C., & Subrahmanyam, M. G. (1995). Multivariate binomial approximations for asset prices with nonstationary variance and covariance characteristics. The Review of Financial Studies, 8(4), 1125-1152. [13] Ho, T. S., & LEE, S. B. (1986). Term structure movements and pricing interest rate contingent claims. The Journal of Finance, 41(5), 1011-1029. [14] Huang, H. C. & Lee, Y. T. (2008). The risk management of interest rate sensitivity policies: Interest rate declaring strategies and investment. 保險專刊, 24, 1-28. [15] Hull, J., & White, A. (1990). Pricing interest-rate-derivative securities. The Review of Financial Studies, 3(4), 573-592. [16] Hull, J., & White, A. (1993). One-factor interest-rate models and the valuation of interest-rate derivative securities. Journal of Financial and Quantitative Analysis, 28(2), 235-254. [17] Hull, J., & White, A. (1994). Numerical procedures for implementing term structure models I: Single-factor models. Journal of Derivatives, 2(1), 7-16. [18] Hull, J., & White, A. (2008). Dynamic models of portfolio credit risk: A simplified approach. Journal of Derivatives, 15(4), 9. [19] Nelson, D. and K. Ramaswamy (1990). Simple binomial processes as diffusion approximations in financial models, The Review of Financial Studies, 3, 393-430. [20] Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of financial Economics, 5(2), 177-188. [21] Wei, J. (1993). Valuing American equity options with a stochastic interest rate: A note, The Journal of Financial Engineering, 2, 195-206. 描述 碩士
國立政治大學
金融學系
105352028資料來源 http://thesis.lib.nccu.edu.tw/record/#G0105352028 資料類型 thesis dc.contributor.advisor 林士貴<br>蔡政憲 zh_TW dc.contributor.advisor Lin, Shih Kuei<br>Tsai, Cheng-Hsien en_US dc.contributor.author (Authors) 林靜吟 zh_TW dc.contributor.author (Authors) Lin, Ching-Yin en_US dc.creator (作者) 林靜吟 zh_TW dc.creator (作者) Lin, Ching-Yin en_US dc.date (日期) 2018 en_US dc.date.accessioned 3-Jul-2018 17:26:44 (UTC+8) - dc.date.available 3-Jul-2018 17:26:44 (UTC+8) - dc.date.issued (上傳時間) 3-Jul-2018 17:26:44 (UTC+8) - dc.identifier (Other Identifiers) G0105352028 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/118240 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 金融學系 zh_TW dc.description (描述) 105352028 zh_TW dc.description.abstract (摘要) 本文在Hull and White隨機利率模型之下計算利率變動型壽險的公平保費及其隱含之解約選擇權。本文提出遞迴公式並逆向計算保單價值，應用條件期望值的方法，建構二維樹狀結構計算利變型壽險的保費。利用本文提出的二維樹狀結構評價，不但具有精確性與收斂特性，計算上也十分有效率。本文也同時分析影響公平保費與解約選擇權價值之各項因子，包含利率波動度，資產波動度，利率和資產相關係數等。分析指出當利率波動劇烈時，利率變動型壽險價值與解約選擇權價值會隨著增加；區隔資產帳戶價值波動度劇烈時，利率變動型壽險價值會隨著減少而解約選擇權價值會隨著增加；最後，利率和區隔資產帳戶價值相關係數越高，利率變動型壽險價值越低，而解約選擇權價值越高。本文提出之評價方法與數值分析結果可供於保險公司評價利率變動型商品之參考。 zh_TW dc.description.abstract (摘要) This paper provides the fair valuation of a floating-rate life insurance policy embedded with surrender options under Hull and White stochastic interest rate models. This paper proposes a recursive formula to implement the backward computation and a two dimensions tree structure is constructed by the Conditional Expectation method to value the fair premiums of floating-rate life insurance policy. By using the proposed algorithm, we analyze the factors affecting the value of premiums and surrender options. Numerical analysis indicates that high interest rate volatility enhances both the premiums and surrender options values entitled to the policyholder. Moreover, when the value of segregate asset account has a high degree of volatility, the premiums of floating-rate life insurance will decrease and the value of surrender options will increase. Finally, the higher the correlation coefficient between the interest rate and the value of segregate asset account, the lower the premiums of floating-rate life insurance, conversely, the higher the value of the surrender options. These results present some suggestions for insurance companies to issue a floating-rate life insurance contract embedded with surrender options. en_US dc.description.tableofcontents 第一章 緒論 1 第一節 研究動機 1 第二節 研究目的 2 第三節 研究架構 2 第二章 文獻探討 3 第一節 短期利率模型 3 第二節 利率變動型保單 4 第三節 二維度樹模型 5 第三章 契約架構 6 第一節 利率變動型壽險的架構 6 第二節 基本契約 7 第三節 宣告利率 8 第四節 解約機制 10 第四章 研究方法 11 第一節 隨機模型 12 第二節 可解約之公平保費與解約選擇權價值 13 第三節 二維度樹模型 15 第五章 數值分析 21 第一節 不可解約利率變動型壽險公平保費 21 第二節 可解約利率變動型壽險公平保費敏感度分析 25 第六章 結論 30 參考文獻 32 附錄一、利率與區隔資產帳戶的條件機率分配 34 附錄二、不可解約公平保費之期望值 36 zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0105352028 en_US dc.subject (關鍵詞) 條件期望值 zh_TW dc.subject (關鍵詞) 利變型保單 zh_TW dc.subject (關鍵詞) Hull and white en_US dc.subject (關鍵詞) Conditional expectation en_US dc.subject (關鍵詞) CRR en_US dc.subject (關鍵詞) Floating-rate insurance policy en_US dc.title (題名) 隨機利率下可解約利率變動型壽險評價分析 zh_TW dc.title (題名) The Valuation Analysis of Floating-rate Life Insurance under Stochastic Interest Rates en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) 一、 中文文獻 [1] 李明黛. (2002). 利率風險對公司經營之影響:台灣壽險市場之實證研究. 政治大學風險管理與保險學系碩士學位論文. [2] 林士貴, 張智凱, & 廖四郎. (2008). 可解約分紅保單之遞迴評價公式. 財務金融學刊, 16(3), 107-147. [3] 賴詩婷. (2011). 隨機利率模型下分紅保單之解約選擇權評價. 逢甲大學統計與精算學系碩士學位論文. [4] 王禕鴻. (2015). 利率變動型壽險探討. 中央大學財務金融學系碩士在職專班學位論文. 二、 英文文獻 [1] Bacinello, A. R., & Ortu, F. (1993). Pricing equity-linked life insurance with endogenous minimum guarantees. Insurance: Mathematics and Economics, 12(3), 245-257. [2] Bacinello, A. R. (2001). Fair pricing of life insurance participating policies with a minimum interest rate guaranteed. ASTIN Bulletin: The Journal of the IAA, 31(2), 275-297. [3] Bacinello, A. R. (2003a). Fair valuation of a guaranteed life insurance participating contract embedding a surrender option. Journal of Risk and Insurance, 70(3), 461-487. [4] Bacinello, A. R. (2003b). Pricing guaranteed life insurance participating policies with annual premiums and surrender option. North American Actuarial Journal, 7(3), 1-17. [5] Bacinello, A. R. (2005). Endogenous model of surrender conditions in equity-linked life insurance. Insurance: Mathematics and Economics, 37(2), 270-296. [6] Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637-654. [7] Briys, E., & De Varenne, F. (1997). On the risk of insurance liabilities: debunking some common pitfalls. Journal of Risk and Insurance, 673-694. [8] Cox, J. C., Ingersoll Jr, J. E., & Ross, S. A. (2005). A theory of the term structure of interest rates. In Theory of Valuation, 129-164. [9] Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7(3), 229-263. [10] Hao, J. C. (2011). The pricing for interest sensitive products of life insurance firms. Scientific Research, 2, 194-202. [11] Hilliard, J., A. Schwartz, and A. Tucker (1996). Bivariate binomial options pricing with generalized interest rate processes. The Journal of Financial Research, 19, 585-602. [12] Ho, T. S., Stapleton, R. C., & Subrahmanyam, M. G. (1995). Multivariate binomial approximations for asset prices with nonstationary variance and covariance characteristics. The Review of Financial Studies, 8(4), 1125-1152. [13] Ho, T. S., & LEE, S. B. (1986). Term structure movements and pricing interest rate contingent claims. The Journal of Finance, 41(5), 1011-1029. [14] Huang, H. C. & Lee, Y. T. (2008). The risk management of interest rate sensitivity policies: Interest rate declaring strategies and investment. 保險專刊, 24, 1-28. [15] Hull, J., & White, A. (1990). Pricing interest-rate-derivative securities. The Review of Financial Studies, 3(4), 573-592. [16] Hull, J., & White, A. (1993). One-factor interest-rate models and the valuation of interest-rate derivative securities. Journal of Financial and Quantitative Analysis, 28(2), 235-254. [17] Hull, J., & White, A. (1994). Numerical procedures for implementing term structure models I: Single-factor models. Journal of Derivatives, 2(1), 7-16. [18] Hull, J., & White, A. (2008). Dynamic models of portfolio credit risk: A simplified approach. Journal of Derivatives, 15(4), 9. [19] Nelson, D. and K. Ramaswamy (1990). Simple binomial processes as diffusion approximations in financial models, The Review of Financial Studies, 3, 393-430. [20] Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of financial Economics, 5(2), 177-188. [21] Wei, J. (1993). Valuing American equity options with a stochastic interest rate: A note, The Journal of Financial Engineering, 2, 195-206. zh_TW dc.identifier.doi (DOI) 10.6814/THE.NCCU.MB.001.2018.F06 -
