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The effect of modelling parameters on the value of GMWB guarantees

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  • Chen, Z.
  • Vetzal, K.
  • Forsyth, P.A.

Abstract

In this article, an extensive study of the no-arbitrage fee for Guaranteed Minimum Withdrawal Benefit (GMWB) variable annuity riders is carried out. The value of the GMWB guarantee increases substantially when taking into account the separation of mutual fund fees and the fees earmarked for hedging the guarantee. In addition, the fee is also adversely affected if the underlying risky asset follows a jump diffusion process. We also explore the effects of various modelling assumptions on the optimal withdrawal strategy of the contract holder, as well as the impact on the guarantee value of sub-optimal withdrawal behaviour. Our general conclusions are that only if several unrealistic modelling assumptions are made is it possible to obtain GMWB fees in the same range as is normally charged. In all other cases, it would appear that typical fees are not enough to cover the cost of hedging these guarantees.

Suggested Citation

  • Chen, Z. & Vetzal, K. & Forsyth, P.A., 2008. "The effect of modelling parameters on the value of GMWB guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 165-173, August.
  • Handle: RePEc:eee:insuma:v:43:y:2008:i:1:p:165-173
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    References listed on IDEAS

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    1. Milevsky, Moshe A. & Salisbury, Thomas S., 2006. "Financial valuation of guaranteed minimum withdrawal benefits," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 21-38, February.
    2. Windcliff, H. & Forsyth, P. A. & Vetzal, K. R., 2001. "Valuation of segregated funds: shout options with maturity extensions," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 1-21, August.
    3. Leif Andersen & Jesper Andreasen, 2000. "Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing," Review of Derivatives Research, Springer, vol. 4(3), pages 231-262, October.
    4. C. He & J. Kennedy & T. Coleman & P. Forsyth & Y. Li & K. Vetzal, 2006. "Calibration and hedging under jump diffusion," Review of Derivatives Research, Springer, vol. 9(1), pages 1-35, January.
    5. Min Dai & Yue Kuen Kwok & Jianping Zong, 2008. "Guaranteed Minimum Withdrawal Benefit In Variable Annuities," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 595-611.
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