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 Policy embedded with Surrender Options under Stochastic Interest Rates

林靜吟(Ching Yin Lin)；蔡政憲(Cheng Hsien Tsai)；林士貴(Shih Kuei Lin)；馮冠群(Kuan Chun Feng)

利變型保單 ； 條件期望值 ； 隨機利率模型 ； Conditional Expectation ； Floating-rate insurance policy ； Stochastic interest rate model

中國統計學報

57卷2期（2019 / 06 / 01）

87 - 119

繁體中文

本文在隨機利率模型之下，計算利率變動型壽險的公平保費及隱含之解約選擇權。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，建構二元樹模型計算利變型壽險的保費。該方法，不但具有精確性與收斂特性，計算上也十分有效率。除此之外，本文也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之增加；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之增加；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。

This paper provides the fair valuation of a floating-rate life insurance policy embedded with surrender options under the stochastic interest rate model. This paper proposes a recursive formula to implement the backward computation and a two dimensions tree structured 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.

1. Bacinello, A. R.(2003).Fair valuation of a guaranteed life insurance participating contract embedding a surrender option.Journal of Risk and Insurance,70(3),461-487.
2. Bacinello, A. R.(2001).Fair pricing of life insurance participating policies with a minimum interest rate guaranteed.The Journal of the IAA,31(2),275-297.
3. Bacinello, A. R.(2003).Pricing guaranteed life insurance participating policies with annual premiums and surrender option.North American Actuarial Journal,7(3),1-17.
4. Black, F.,Scholes, M.(1973).The pricing of options and corporate liabilities.Journal of Political Economy,81(3),637-654.
5. Briys, E.,De Varenne, F.(1997).On the risk of insurance liabilities: debunking some common pitfalls.Journal of Risk and Insurance,673-694.
6. Cox, J. C.,Ingersoll, J. E., Jr,Ross, S. A.(2005).A theory of the term structure of interest rates.Theory of Valuation
7. Cox, J. C.,Ross, S. A.,Rubinstein, M.(1979).Option pricing: A simplified approach.Journal of Financial Economics,7(3),229-263.
8. Hao, J. C.(2011).The pricing for interest sensitive products of life insurance firms.Scientific Research,2,194-202.
9. Hilliard, J.,Schwartz, A.,Tucker A.(1996).Bivariate binomial options pricing with generalized interest rate processes.The Journal of Financial Research,19,585-602.
10. Ho, T. S.,LEE, S. B.(1986).Term structure movements and pricing interest rate contingent claims.The Journal of Finance,41(5),1011-1029.
11. 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.
12. 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.
13. Hull, J.,White, A.(1994).Numerical procedures for implementing term structure models I: Single-factor models.Journal of Derivatives,2(1),7-16.
14. Hull, J.,White, A.(1990).Pricing interest-rate-derivative securities.The Review of Financial Studies,3(4),573-592.
15. Nelson, C.,Siegel, A.F(1987).Parsimonious Modeling of Yield Curves.The Journal of Business,60(4),473-489.
16. Nelson, D.,Ramaswamy, K.(1990).Simple binomial processes as diffusion approximations in financial models.The Review of Financial Studies,3,393-430.
17. Vasicek, O.(1977).An equilibrium characterization of the term structure.Journal of financial Economics,5(2),177-188.
18. Wei, J.(1993).Valuing American equity options with a stochastic interest rate: A note.The Journal of Financial Engineering,2,195-206.
19. 李明黛(2002)。政治大學風險管理與保險學系。
20. 賴詩婷(2011)。逢甲大學統計與精算學系。