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Pricing maturity guarantee with dynamic withdrawal benefit

Author

Listed:
  • Ko, Bangwon
  • Shiu, Elias S.W.
  • Wei, Li

Abstract

Motivated by the importance of withdrawal benefits for enhancing sales of variable annuities, we propose a new equity-linked product which provides a dynamic withdrawal benefit (DWB) during the contract period and a minimum guarantee at contract maturity. The term DWB is coined to reflect the duality between it and dynamic fund protection. Under the Black-Scholes framework and using results pertaining to reflected Brownian motion, we obtain explicit pricing formulas for the DWB payment stream and the maturity guarantee. These pricing formulas are also derived by means of Esscher transforms, which is another seminal contribution by Gerber to finance. In particular, we show that there are closed-form formulas for pricing European put and call options on a traded asset whose price can be modeled as the exponential of a reflected Brownian motion.

Suggested Citation

  • Ko, Bangwon & Shiu, Elias S.W. & Wei, Li, 2010. "Pricing maturity guarantee with dynamic withdrawal benefit," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 216-223, October.
  • Handle: RePEc:eee:insuma:v:47:y:2010:i:2:p:216-223
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    References listed on IDEAS

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    1. Leung, Kwai Sun & Kwok, Yue Kuen & Leung, Seng Yuen, 2008. "Finite-time dividend-ruin models," Insurance: Mathematics and Economics, Elsevier, pages 154-162.
    2. Gerber, Hans U. & Shiu, Elias S. W., 1996. "Actuarial bridges to dynamic hedging and option pricing," Insurance: Mathematics and Economics, Elsevier, pages 183-218.
    3. Lee, Hangsuck, 2003. "Pricing equity-indexed annuities with path-dependent options," Insurance: Mathematics and Economics, Elsevier, pages 677-690.
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    5. Gerber, Hans U. & Shiu, Elias S. W., 1999. "From ruin theory to pricing reset guarantees and perpetual put options," Insurance: Mathematics and Economics, Elsevier, pages 3-14.
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    Citations

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    Cited by:

    1. Zhou, Jiang & Wu, Lan, 2015. "The time of deducting fees for variable annuities under the state-dependent fee structure," Insurance: Mathematics and Economics, Elsevier, pages 125-134.
    2. repec:wly:jmoncb:v:49:y:2017:i:2-3:p:567-578 is not listed on IDEAS
    3. Hertrich Markus, 2016. "The Costs of Implementing a Unilateral One-Sided Exchange Rate Target Zone," Review of Economics, De Gruyter, pages 91-120.
    4. Hertrich Markus, 2016. "The Costs of Implementing a Unilateral One-Sided Exchange Rate Target Zone," Review of Economics, De Gruyter, pages 91-120.
    5. Gerber, Hans U. & Shiu, Elias S.W. & Yang, Hailiang, 2013. "Valuing equity-linked death benefits in jump diffusion models," Insurance: Mathematics and Economics, Elsevier, pages 615-623.
    6. Markus Hertrich & Heinz Zimmermann, 2015. "On the Credibility of the Euro/Swiss Franc Floor: A Financial Market Perspective," Working papers 2015/09, Faculty of Business and Economics - University of Basel.
    7. Zhou, Jiang & Wu, Lan, 2015. "Valuing equity-linked death benefits with a threshold expense strategy," Insurance: Mathematics and Economics, Elsevier, pages 79-90.
    8. Han, Heejae & Jeon, Junkee & Kang, Myungjoo, 2016. "Pricing chained dynamic fund protection," The North American Journal of Economics and Finance, Elsevier, vol. 37(C), pages 267-278.
    9. Gan, Guojun, 2013. "Application of data clustering and machine learning in variable annuity valuation," Insurance: Mathematics and Economics, Elsevier, pages 795-801.
    10. Gerber, Hans U. & Shiu, Elias S.W. & Yang, Hailiang, 2012. "Valuing equity-linked death benefits and other contingent options: A discounted density approach," Insurance: Mathematics and Economics, Elsevier, pages 73-92.

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