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Valuation of power option for uncertain financial market

Author

Listed:
  • Zhang, Zhiqiang
  • Liu, Weiqi
  • Sheng, Yuhong

Abstract

Power option is such an option whose payoff is based on the price of the underlying asset raised to some power. Unlike Black–Scholes setting, we investigate the valuation of power options under the assumption that the underlying stock price is assumed to follow an uncertain differential equation, and derive the pricing formulas of power options for Liu’s uncertain stock model with the method of uncertain calculus based on uncertainty theory. Some numerical examples are given to illustrate the pricing formulas.

Suggested Citation

  • Zhang, Zhiqiang & Liu, Weiqi & Sheng, Yuhong, 2016. "Valuation of power option for uncertain financial market," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 257-264.
    • Handle: RePEc:eee:apmaco:v:286:y:2016:i:c:p:257-264
    DOI: 10.1016/j.amc.2016.04.032
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    References listed on IDEAS

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    Cited by:

    1. Yang, Xiangfeng & Zhang, Zhiqiang & Gao, Xin, 2019. "Asian-barrier option pricing formulas of uncertain financial market," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 79-86.
    2. Lu, Jing & Yang, Xiangfeng & Tian, Miao, 2022. "Barrier swaption pricing formulae of mean-reverting model in uncertain environment," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    3. Foad Shokrollahi, 2017. "Valuation of equity warrants for uncertain financial market," Papers 1711.08356, arXiv.org, revised Nov 2017.
    4. Marcos Escobar-Anel & Eric Molter & Rudi Zagst, 2024. "The power of derivatives in portfolio optimization under affine GARCH models," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 151-181, June.
    5. Tsvetelin S. Zaevski, 2024. "Quadratic American Strangle Options in Light of Two-Sided Optimal Stopping Problems," Mathematics, MDPI, vol. 12(10), pages 1-27, May.
    6. Yang, Xiangfeng & Liu, Yuhan & Park, Gyei-Kark, 2020. "Parameter estimation of uncertain differential equation with application to financial market," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    7. Liu, Yang & Lio, Waichon, 2024. "Power option pricing problem of uncertain exponential Ornstein–Uhlenbeck model," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    8. Pan, Zeyu & Gao, Yin & Yuan, Lin, 2021. "Bermudan options pricing formulas in uncertain financial markets," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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