可解約分紅保單之遞迴評價公式

A Recursive Formula of a Participating Contract Embedding a Surrender Option

10.6545/JFS.2008.16(3).4

林士貴(Shih-Kuei Lin)；張智凱(Chih-Kai Chang)；廖四郎(Szu-Lang Liao)

分紅係單 ； 分紅選擇權 ； 解約選擇權 ； 二維度CRR模型 ； Participating Policy ； participating Option ； surrender Option ； two-dimensional CRR Model

財務金融學刊

16卷3期（2008 / 09 / 30）

107 - 147

繁體中文

Bacinello（2003a）於固定利率之下評價分紅保單，此分紅保單包含分紅選擇權與解約選擇權，分紅選擇權可視為歐式選擇權，解約選擇權可視為美式選擇榷。本文在隨機利率模型下，提出二維度CRR模型，以評價分紅選擇權與解約選擇權，不但具有精確度與收斂性質，而且在計算上也十分有效率。此外，本文針對分紅係單中現金流量之前後關係，推導出遞迴關係式，以增進二維度CRR模型之計算速度。根據二維度CRR模型之遞迴公式，求得可解約分紅保單之公平價值，並討論各種參數對可解約分紅保單的影響，以利於保險公司評價可解約分紅保單之參考。

Bacinello (2003a) employed CRR model to numerically calculate the fair value of a participating policy containing a surrender option. Bacinello assumed a constant rate of return on risk-free assets. However, this study proposes a two-dimensional CU model in a stochastic interest rate model as a means of providing a numerical method for contract pricing. The two-dimensional CU model converges rapidly and achieves similar results to Monte Carlo simulation. Two-dimensional CU models are used to analyze the importance and sensitivity of a stochastic interest rate model for the policy. Zero coupon bond volatility is an essential parameter in the surrender option, and reference portfolio volatility is important for pricing the participating option. The participating and surrender options are more valuable given upwards trending interest rates than constant or downwards trending rates.

1. Albizzati, M.-O.,Geman, H.(1994).Interest Rate Management and Valuation of the Surrender Option in Life Insurance Policies.Journal of Risk and Insurance,61(4),616-637.
2. Bacinello, A. R.(2005).Endogenous model of surrender conditions in equity-linked life insurance.Insurance: Mathematics and Economics,37,270-296.
3. 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.
4. Bacinello, A. R.(2003).Pricing Guaranteed Life Insurance Participating Policies with Annual Premiums and Surrender Option.North American Actuarial Journal,7(3),1-11.
5. Bacinello, A. R.(2001).Fair Pricing of Life Insurance Participating Polices with a Minimum Interest Rate Guaranteed.ASTIN Bulletin,31(2),275-297.
6. Bacinello, A. R.,Ortu, F.(1993).Pricing Equity-linked Life Insurance with Endogenous Minimum Guarantees.Insurance: Mathematics and Economics,12,245-257.
7. Benjamin, J.,Soliman, A. S.(1993).Actuarial Education Service.Oxford:
8. Black, F.,Scholes, M.(1973).The Pricing of Options and Corporate Liabilities.Journal of Political Economy,81(3),637-654.
9. Bowers, N. L.,Gerber, H. U.,Hickman, J. C.,Jones, D. A.,Nesbitt, C. J.(1986).Actuarial Mathematics.Society of Actuaries.
10. Boyle, P. P.,E. S. Schwartz(1977).Equilibrium Prices of Guarantees under Equity-Linked Contracts.Journal Risk and Insurance,44(4),639-660.
11. Brennan, M. J.,Schwartz, E, S.(1979).Monograph no 7/ The S. S. Huebner Foundation for Insurance Education.Philadelphia:Wharton School, University of Pennsylvania.
12. Brennan, M. J.,Schwartz, E. S.(1979).Alternative Investment Strategies for the Issuers of Equity Linked Life Insurance with an Asset Value Guarantee.Journal of Business,52,63-93.
13. Brennan, M. J.,Schwartz, E. S.(1976).The Pricing of Equity-Linked Life Insurance Policies with an Asset Value Guarantee.Journal of Financial Economics,3,15-213.
14. Briys, E.,de Varenne, F.(1997).On The Risk of Life Insurance Liabilities: Debunking Some Common Pitfalls.Journal of Risk and Insurance,64(4),673-694.
15. Cox, J. C.,Ingersoll, J. E.,Ross, S. A.(1985).A Theory of The Term Structure of Interest Rates.Econometrica,53,385-407.
16. Cox, J. C.,Ross, S. A.,Rubinstein, M.(1979).Option Pricing: A Simplified Approach.Journal of Financial Economics,7,229-263.
17. Delbaen, F.(1990).Equity Linked Policies.Bulletin Association des Actuaries Belges,33-52.
18. Gorgensen, P. L.(2004).n accounting standards and fair valuation of life insurance and pension liabilities.Scandinavian Actuarial Journal,5,372-394.
19. Grosen, A.,Jorgensen, P. L.(1997).Valuation of Early Exercisable Interest Rate Guarantees.Journal of Risk and Insurance,64(3),481-503.
20. Grosen, A.,Jorgensen, P. L.(2000).Fair Valuation of Life Insurance Liabilities: the Impact of Interest Rate Guarantees, Surrender Options, and Bonus Policies.Insurance: Mathematics and Economics,26(1),37-57.
21. Heath, D.,Jarrow, R.,Morton, A. J.(1992).Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation.Econometrica,60,77-105.
22. Ho, T. S.,Lee, S.(1986).Term Structure Movement and Pricing Interest Rate Contingent Claim.Journal of Finance,41,1011-1028.
23. Hull, J.,White, A.(1990).Pricing Interest Rate Derivative Securities.Review of Financial Studies,3,573-592.
24. Macdonald, A. S.,Cairns, A. J. G.,Gwilt, P. L.,Miller, K. A.(1998).An International Comparison of Recent Trends in Population Mortality.British Actuarial Journal,4,3-141.
25. Miltersen, K. R.,Persson, S.-A.(2000).Working Paper.Department of Finance and Management Science, Norwegian School of Economics and Business Administration.
26. Miltersen, K. R.,Persson, S.-A.(2000).A Note on Interest Rate Guarantees and Bonus: The Norwegian Case.Proceedings of the Tenth AFIR International Colloquium, Tromso,507-516.
27. Nielsen, J. A.(1993).Equity-linked Life Insurance Contracts in an Economy with a Stochastic Development of the term Structure of Interest Rates.Department of Operations Research, Aarhus Universtiy.
28. Vasicek, O.(1977).An Equilibrium Characterization of the Term Structure.Journal of Financial Economics,5,177-188.

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