Stochastic Interest Rate Approach of Pricing Participating Life Insurance Policies with Embedded Surrender Option
American Journal of Mathematical and Computer Modelling
Volume 3, Issue 1, March 2018, Pages: 10-21
Received: Feb. 15, 2018;
Accepted: Mar. 9, 2018;
Published: Apr. 8, 2018
Views 1374 Downloads 86
Mustapha Abdul-Rahaman, Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
Francis Oduro, Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
Al-Hassan Issahaku, Department of Informatics, Regent University College of Science and Technology, Accra, Ghana
Life insurance contracts are priced and analysed using techniques from actuarial and modern financial mathematics, which requires that, the conditions for the risk-neutral valuation are fulfilled and that, a specified underlying security and an equivalent martingale measure must exist. This paper analysed life insurance endowment policy, paid by sequence of periodical premiums in Ghana with a guaranteed minimum return to the policyholder. Again, this paper presents two premium determination schemes for the insurance policy, the constant premium case and the periodical adjustment case in which both the benefit and the periodical premiums are annually adjusted in relation to the performance of a reference portfolio. It was realized that, with rising guaranteed interest rate, the rate of return on the reference portfolio, the premiums of the whole contract decreased both in the constant and the periodical adjustment cases whiles an increase in the participating coefficient and age of the insured led to an increase in the whole premium both in the constant and periodical adjustment cases. Also, it was revealed that, the premium of the non-surrendered bonus option is smaller in the constant premium case than in the periodical adjustment case and the premium of the bonus option in the surrendered participating policy looks cheap in the constant premium case than in the periodical adjustment case. Thus, it’s about 1.03% and 6.95% respectively of the total premium for the constant and for the periodical adjustment cases.
Stochastic Interest Rate Approach of Pricing Participating Life Insurance Policies with Embedded Surrender Option, American Journal of Mathematical and Computer Modelling.
Vol. 3, No. 1,
2018, pp. 10-21.
Bacinello, A. R. (2001). Fair pricing of life insurance participating policies with a minimum interest rate guaranteed. Astin Bulletin, 31(02): 275–297.
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.
Ballotta, L., Haberman, S., & Wang, N. (2006). Guarantees in With-Profit and Unitized With-Profit Life Insurance Contracts: Fair Valuation Problem in Presence of the Default Option. Journal of Risk and Insurance, 73(1): 97–121.
Bauer, D., Kling, A., & Russ, J. (2008). A universal pricing framework for guaranteed minimum benefits in variable annuities. Astin Bulletin, 38(02): 621–651.
Bernard, C., & Lemieux, C. (2008). Fast simulation of equity-linked life insurance contracts with a surrender option. In Proceedings of the 40th Conference on Winter Simulation (pp.444–452). Winter Simulation Conference. Retrieved from http://dl.acm.org/citation.cfm?id=1516831
Biener, C. (2013). Pricing in microinsurance markets. World Development, 41:132–144.
Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. The Journal of Political Economy, pages 637–654.
Bowers, N. L., Gerber, H. U., Hickman, J. C., Jones, D. A., & Nesbitt, C. J. (1986). Actuarial mathematics (Vol. 2). Society of Actuaries Itasca, Ill. Retrieved from http://www.sidalc.net/cgibin/wxis.exe/?IsisScript=FCEAL.xis&method=post&formato=2&cantidad=1&expresion=mfn=004732
Briys, E., & De Varenne, F. (1997). On the risk of insurance liabilities: debunking some common pitfalls. Journal of Risk and Insurance, pages 673–694.
Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7(3): 229–263.
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.
Jensen, B., Jorgensen, P. L., & Grosen, A. (2001). A finite difference approach to the valuation of path dependent life insurance liabilities. The Geneva Papers on Risk and Insurance Theory, 26(1): 57–84.
Jorgensen, P. L. (2001). Life Insurance Contracts with Embedded Options: Valuation, Risk Management, and Regulation. Risk Management, and Regulation (December 13, 2012). Journal of Risk Finance, 3(1): 19–30.
Liao, S.-L., Chang, C.-K., & Lin, S.-K. (2006). Fair Valuation of Participating Policies in Stochastic Interest Rate Models: Two-dimensional Cox-Ross-Rubinstein Approaches. Retrieved from http://www.aria.org/meetings/2006papers/Liao, Szu-LangChi-KaiShih-Kuei.pdf
Merton, R. C. (1973). Theory of rational option pricing, The Bell Journal of Economics and Management Science 4 (1): 141–183. URL: Http://www. Jstor. org/stable/3003143.
Miltersen, K. R., & Persson, S.-A. (2003). Guaranteed investment contracts: distributed and undistributed excess return. Scandinavian Actuarial Journal, 2003(4): 257–279.
Nielsen, J. A., & Sandmann, K. (1995). Equity-linked life insurance: A model with stochastic interest rates. Insurance: Mathematics and Economics, 16(3): 225–253.
Wang, S. (1995). Insurance pricing and increased limits ratemaking by proportional hazards transforms. Insurance: Mathematics and Economics, 17(1): 43–54.
Zaglauer, K., & Bauer, D. (2008). Risk-neutral valuation of participating life insurance contracts in a stochastic interest rate environment. Insurance: Mathematics and Economics, 43(1): 29–40.