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Quantile hedging on equity-linked life insurance contracts with transaction costs

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  • Melnikov, Alexander
  • Tong, Shuo

Abstract

This paper analyzes the application of quantile hedging on equity-linked life insurance contracts in the presence of transaction costs. Following the time-based replication strategy, we present the explicit expressions for the present values of expected hedging errors and transaction costs. The results are derived by using the adjusted hedging volatility σ̄ proposed by Leland. Furthermore, the estimated values of expected hedging errors, transaction costs and total costs are obtained from a simulation approach for comparison. Finally, the costs of maturity guarantee for equity-linked life insurance contracts inclusive of transaction costs are discussed.

Suggested Citation

  • Melnikov, Alexander & Tong, Shuo, 2014. "Quantile hedging on equity-linked life insurance contracts with transaction costs," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 77-88.
    • Handle: RePEc:eee:insuma:v:58:y:2014:i:c:p:77-88
    DOI: 10.1016/j.insmatheco.2014.06.005
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    References listed on IDEAS

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    1. Leland, Hayne E, 1985. "Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
    2. Edirisinghe, Chanaka & Naik, Vasanttilak & Uppal, Raman, 1993. "Optimal Replication of Options with Transactions Costs and Trading Restrictions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(1), pages 117-138, March.
    3. Steinar Ekern & Svein-Arne Persson, 1996. "Exotic Unit-Linked Life Insurance Contracts," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 21(1), pages 35-63, June.
    4. Melnikov, Alexander & Romaniuk, Yulia, 2006. "Evaluating the performance of Gompertz, Makeham and Lee-Carter mortality models for risk management with unit-linked contracts," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 310-329, December.
    5. Yuri M. Kabanov & (*), Mher M. Safarian, 1997. "On Leland's strategy of option pricing with transactions costs," Finance and Stochastics, Springer, vol. 1(3), pages 239-250.
    6. Mary Hardy, 2000. "Hedging and Reserving for Single-Premium Segregated Fund Contracts," North American Actuarial Journal, Taylor & Francis Journals, vol. 4(2), pages 63-74.
    7. Zhao, Yonggan & Ziemba, William T., 2007. "Hedging errors with Leland's option model in the presence of transaction costs," Finance Research Letters, Elsevier, vol. 4(1), pages 49-58, March.
    8. Bernard Bensaid & Jean‐Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs1," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86, April.
    9. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
    10. Brennan, Michael J & Schwartz, Eduardo S, 1979. "Alternative Investment Strategies for the Issuers of Equity Linked Life Insurance Policies with an Asset Value Guarantee," The Journal of Business, University of Chicago Press, vol. 52(1), pages 63-93, January.
    11. Toft, Klaus Bjerre, 1996. "On the Mean-Variance Tradeoff in Option Replication with Transactions Costs," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(2), pages 233-263, June.
    12. Alexander Melnikov & Yuliya Romanyuk, 2008. "Efficient Hedging And Pricing Of Equity-Linked Life Insurance Contracts On Several Risky Assets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(03), pages 295-323.
    13. Boyle, Phelim P & Vorst, Ton, 1992. "Option Replication in Discrete Time with Transaction Costs," Journal of Finance, American Finance Association, vol. 47(1), pages 271-293, March.
    14. Brennan, Michael J. & Schwartz, Eduardo S., 1976. "The pricing of equity-linked life insurance policies with an asset value guarantee," Journal of Financial Economics, Elsevier, vol. 3(3), pages 195-213, June.
    15. Boyle, Phelim P. & Hardy, Mary R., 1997. "Reserving for maturity guarantees: Two approaches," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 113-127, November.
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    Cited by:

    1. Barski Michał, 2016. "On the shortfall risk control: A refinement of the quantile hedging method," Statistics & Risk Modeling, De Gruyter, vol. 32(2), pages 125-141, March.
    2. Gan, Guojun & Valdez, Emiliano A., 2017. "Modeling partial Greeks of variable annuities with dependence," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 118-134.

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