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Efficient Hedging And Pricing Of Equity-Linked Life Insurance Contracts On Several Risky Assets

Author

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  • ALEXANDER MELNIKOV

    (Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada)

  • YULIYA ROMANYUK

    (Financial Markets Department, Bank of Canada, 234 Wellington, Ottawa, Ontario K1A OG9, Canada)

Abstract

The paper uses the efficient hedging methodology in order to optimally price and hedge equity-linked life insurance contracts whose payoff depends on the performance of several risky assets. In particular, we consider a policy which pays the maximum of the values of n risky assets at some maturity date T, provided that the policyholder survives to T. Such contracts incorporate financial risk, which stems from the uncertainty about future prices of the underlying financial assets, and insurance risk, which arises from the policyholder's mortality. We show how efficient hedging can be used to minimize expected losses from imperfect hedging under a particular risk preference of the hedger. We also prove a probabilistic result, which allows one to calculate analytic pricing formulas for equity-linked payoffs with n risky assets. To illustrate its use, explicit formulas are given for optimal prices and expected hedging losses for payoffs with two risky assets. Numerical examples highlighting the implications of efficient hedging for the management of financial and insurance risks of equity-linked life insurance policies are also provided.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:11:y:2008:i:03:n:s0219024908004816
    DOI: 10.1142/S0219024908004816
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    Citations

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    Cited by:

    1. Feng, Runhuan & Shimizu, Yasutaka, 2016. "Applications of central limit theorems for equity-linked insurance," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 138-148.
    2. Klusik Przemyslaw, 2014. "Hedging of equity-linked with maximal success factor," Papers 1405.0732, arXiv.org.
    3. Leunglung Chan & Eckhard Platen, 2016. "Pricing of long dated equity-linked life insurance contracts," Published Paper Series 2016-5, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    4. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. Kevin Fergusson & Eckhard Platen, 2017. "Less-Expensive Valuation of Long Term Annuities Linked to Mortality, Cash and Equity," Papers 1711.02808, arXiv.org.
    6. Belssing Taruvinga, 2019. "Solving Selected Problems on American Option Pricing with the Method of Lines," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 4-2019, January-A.
    7. Gao, Quansheng & He, Ting & Zhang, Chi, 2011. "Quantile hedging for equity-linked life insurance contracts in a stochastic interest rate economy," Economic Modelling, Elsevier, vol. 28(1), pages 147-156.
    8. Gao, Quansheng & He, Ting & Zhang, Chi, 2011. "Quantile hedging for equity-linked life insurance contracts in a stochastic interest rate economy," Economic Modelling, Elsevier, vol. 28(1-2), pages 147-156, January.
    9. Kevin Fergusson & Eckhard Platen, 2013. "Real World Pricing of Long Term Cash-Linked Annuities and Equity-Linked Annuities with Cash-Linked Guarantees," Research Paper Series 338, Quantitative Finance Research Centre, University of Technology, Sydney.
    10. 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.
    11. Alexander Melnikov & Amir Nosrati, 2015. "Efficient Hedging For Defaultable Securities And Its Application To Equity-Linked Life Insurance Contracts," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(07), pages 1-28, November.
    12. Klusik, Przemyslaw & Palmowski, Zbigniew, 2011. "Quantile hedging for equity-linked contracts," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 280-286, March.
    13. 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.
    14. Melnikov, Alexander & Tong, Shuo, 2014. "Valuation of finance/insurance contracts: Efficient hedging and stochastic interest rates modeling," Risk and Decision Analysis, IOS Press, issue 5, pages 23-41.

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    More about this item

    Keywords

    Efficient hedging; equity-linked insurance; multi-asset theorem;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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