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Efficient Hedging and Pricing of Equity-Linked Life Insurance Contracts on Several Risky Assets

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  • Alexander Melnikov
  • Yuliya Romanyuk

Abstract

The authors use the efficient hedging methodology for optimal pricing and hedging of equitylinked life insurance contracts whose payoff depends on the performance of several risky assets. In particular, they consider a policy that 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. The authors show how efficient hedging can be used to minimize expected losses from imperfect hedging under a particular risk preference of the hedger. They 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 derived 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.

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Bibliographic Info

Paper provided by Bank of Canada in its series Working Papers with number 06-43.

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Length: 66 pages
Date of creation: 2006
Date of revision:
Handle: RePEc:bca:bocawp:06-43

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Keywords: Financial markets;

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References

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  1. Elisa Luciano & Elena Vigna, 2006. "Non mean reverting affne processes for stochastic mortality," Carlo Alberto Notebooks, Collegio Carlo Alberto 30, Collegio Carlo Alberto.
  2. 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, Elsevier, vol. 3(3), pages 195-213, June.
  3. 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.
  4. Bacinello, Anna Rita & Ortu, Fulvio, 1993. "Pricing equity-linked life insurance with endogenous minimum guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 12(3), pages 245-257, June.
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  7. Boyle, Phelim P. & Lin, X. Sheldon, 1997. "Bounds on contingent claims based on several assets," Journal of Financial Economics, Elsevier, Elsevier, vol. 46(3), pages 383-400, December.
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  9. Nakano, Yumiharu, 2004. "Minimization of shortfall risk in a jump-diffusion model," Statistics & Probability Letters, Elsevier, vol. 67(1), pages 87-95, March.
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  12. Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 113-136, August.
  13. Ioannis Karatzas & Jaksa Cvitanic, 1999. "On dynamic measures of risk," Finance and Stochastics, Springer, vol. 3(4), pages 451-482.
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Cited by:
  1. 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.
  2. Klusik Przemyslaw, 2014. "Hedging of equity-linked with maximal success factor," Papers 1405.0732, arXiv.org.
  3. Klusik, Przemyslaw & Palmowski, Zbigniew, 2011. "Quantile hedging for equity-linked contracts," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 280-286, March.
  4. 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, Quantitative Finance Research Centre, University of Technology, Sydney 338, Quantitative Finance Research Centre, University of Technology, Sydney.
  5. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 262, Quantitative Finance Research Centre, University of Technology, Sydney.

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