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Stochastic Interest Rate Approach of Pricing Participating Life Insurance Policies with Embedded Surrender Option

Received: 15 February 2018     Accepted: 9 March 2018     Published: 8 April 2018
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Abstract

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.

Published in American Journal of Mathematical and Computer Modelling (Volume 3, Issue 1)
DOI 10.11648/j.ajmcm.20180301.12
Page(s) 10-21
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Stochastic Interest Rate, Surrender Option, Participating Policies, Life Insurance Policy, Periodical Premiums

References
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[2] 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.
[3] 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.
[4] Bauer, D., Kling, A., & Russ, J. (2008). A universal pricing framework for guaranteed minimum benefits in variable annuities. Astin Bulletin, 38(02): 621–651.
[5] 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
[6] Biener, C. (2013). Pricing in microinsurance markets. World Development, 41:132–144.
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[9] Briys, E., & De Varenne, F. (1997). On the risk of insurance liabilities: debunking some common pitfalls. Journal of Risk and Insurance, pages 673–694.
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[11] 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.
[12] 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.
[13] 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.
[14] 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
[15] 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.
[16] Miltersen, K. R., & Persson, S.-A. (2003). Guaranteed investment contracts: distributed and undistributed excess return. Scandinavian Actuarial Journal, 2003(4): 257–279.
[17] Nielsen, J. A., & Sandmann, K. (1995). Equity-linked life insurance: A model with stochastic interest rates. Insurance: Mathematics and Economics, 16(3): 225–253.
[18] Wang, S. (1995). Insurance pricing and increased limits ratemaking by proportional hazards transforms. Insurance: Mathematics and Economics, 17(1): 43–54.
[19] 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.
Cite This Article
  • APA Style

    Mustapha Abdul-Rahaman, Francis Oduro, Al-Hassan Issahaku. (2018). Stochastic Interest Rate Approach of Pricing Participating Life Insurance Policies with Embedded Surrender Option. American Journal of Mathematical and Computer Modelling, 3(1), 10-21. https://doi.org/10.11648/j.ajmcm.20180301.12

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    ACS Style

    Mustapha Abdul-Rahaman; Francis Oduro; Al-Hassan Issahaku. Stochastic Interest Rate Approach of Pricing Participating Life Insurance Policies with Embedded Surrender Option. Am. J. Math. Comput. Model. 2018, 3(1), 10-21. doi: 10.11648/j.ajmcm.20180301.12

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    AMA Style

    Mustapha Abdul-Rahaman, Francis Oduro, Al-Hassan Issahaku. Stochastic Interest Rate Approach of Pricing Participating Life Insurance Policies with Embedded Surrender Option. Am J Math Comput Model. 2018;3(1):10-21. doi: 10.11648/j.ajmcm.20180301.12

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  • @article{10.11648/j.ajmcm.20180301.12,
      author = {Mustapha Abdul-Rahaman and Francis Oduro and Al-Hassan Issahaku},
      title = {Stochastic Interest Rate Approach of Pricing Participating Life Insurance Policies with Embedded Surrender Option},
      journal = {American Journal of Mathematical and Computer Modelling},
      volume = {3},
      number = {1},
      pages = {10-21},
      doi = {10.11648/j.ajmcm.20180301.12},
      url = {https://doi.org/10.11648/j.ajmcm.20180301.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20180301.12},
      abstract = {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.},
     year = {2018}
    }
    

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  • TY  - JOUR
    T1  - Stochastic Interest Rate Approach of Pricing Participating Life Insurance Policies with Embedded Surrender Option
    AU  - Mustapha Abdul-Rahaman
    AU  - Francis Oduro
    AU  - Al-Hassan Issahaku
    Y1  - 2018/04/08
    PY  - 2018
    N1  - https://doi.org/10.11648/j.ajmcm.20180301.12
    DO  - 10.11648/j.ajmcm.20180301.12
    T2  - American Journal of Mathematical and Computer Modelling
    JF  - American Journal of Mathematical and Computer Modelling
    JO  - American Journal of Mathematical and Computer Modelling
    SP  - 10
    EP  - 21
    PB  - Science Publishing Group
    SN  - 2578-8280
    UR  - https://doi.org/10.11648/j.ajmcm.20180301.12
    AB  - 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.
    VL  - 3
    IS  - 1
    ER  - 

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Author Information
  • Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana

  • Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana

  • Department of Informatics, Regent University College of Science and Technology, Accra, Ghana

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