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Pricing of Equity Indexed Annuity under Fractional Brownian Motion Model

Author

Listed:
  • Lin Xu
  • Guangjun Shen
  • Dingjun Yao

Abstract

Fractional Brownian motion with Hurst exponent H ∈ (1/2, 1) is a good candidate for modeling financial time series with long‐range dependence and self‐similarity. The main purpose of this paper is to address the valuation of equity indexed annuity (EIA) designs under the market driven by fractional Brownian motion. As a result, this paper presents an explicit pricing expression for point‐to‐point EIA design and bounds for the pricing of high‐water‐marked EIA design. Some numerical examples are given to illustrate the impact of the parameters involved in the pricing problems.

Suggested Citation

  • Lin Xu & Guangjun Shen & Dingjun Yao, 2014. "Pricing of Equity Indexed Annuity under Fractional Brownian Motion Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:380718
    DOI: 10.1155/2014/380718
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    References listed on IDEAS

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    1. Zbigniew Michna, 1998. "Self-similar processes in collective risk theory," International Journal of Stochastic Analysis, Hindawi, vol. 11, pages 1-20, January.
    2. Qian, Linyi & Wang, Wei & Wang, Rongming & Tang, Yincai, 2010. "Valuation of equity-indexed annuity under stochastic mortality and interest rate," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 123-129, October.
    3. Moore, Kristen S., 2009. "Optimal surrender strategies for equity-indexed annuity investors," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 1-18, February.
    4. Lee, Hangsuck, 2003. "Pricing equity-indexed annuities with path-dependent options," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 677-690, December.
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