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Pricing Variable Annuity Contracts with High-Water Mark Feature

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  • V. M. Belyaev
Abstract
Variable annuities (VA) are popular insurance products. VAs provides the insured with a guaranteed accumulation rate on their premium at maturity. In addition, the insured may receive extra benefit if returns of underlying funds are high enough. Here we consider a special case of VA with high-water mark feature and Guaranteed Minimum payment reset. In Black-Scholes model for underlying fund we derive explicit pricing formula for this type of contract. The value of VA contracts depends on the time between observation dates. Corrections due to this effect are calculated and compared with Monte-Carlo results. Good agreement between analytical formula and numerical calculations of VA values is demonstrated.

Suggested Citation

  • V. M. Belyaev, 2011. "Pricing Variable Annuity Contracts with High-Water Mark Feature," Papers 1108.4393, arXiv.org, revised Aug 2011.
    • Handle: RePEc:arx:papers:1108.4393
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    References listed on IDEAS

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    1. Lee, Hangsuck, 2003. "Pricing equity-indexed annuities with path-dependent options," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 677-690, December.
    2. Serena Tiong, 2000. "Valuing Equity-Indexed Annuities," North American Actuarial Journal, Taylor & Francis Journals, vol. 4(4), pages 149-163.
    3. 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.
    4. Hans Gerber & Elias Shiu, 2003. "Pricing Lookback Options and Dynamic Guarantees," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(1), pages 48-66.
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