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Barrier option pricing of mean-reverting stock model in uncertain environment

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  • Tian, Miao
  • Yang, Xiangfeng
  • Zhang, Yi

Abstract

The barrier options become activated or extinguished only if the underlying asset’s price reaches a predetermined level. Options of the former case are the knock-in options, and options of the latter case are the knock-out options. Barrier options are a type of path-dependent options which have a big difference from the path-independent options, such as European options and American options. This paper studies the barrier options based on the mean-reverting stock model in uncertain environment. The four types of European barrier options pricing formulas, which are up-and-in call options, down-and-in put options, up-and-out put options, and down-and-out call options, are derived and the corresponding numerical algorithms are designed to compute the prices of these options.

Suggested Citation

  • Tian, Miao & Yang, Xiangfeng & Zhang, Yi, 2019. "Barrier option pricing of mean-reverting stock model in uncertain environment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 126-143.
    • Handle: RePEc:eee:matcom:v:166:y:2019:i:c:p:126-143
    DOI: 10.1016/j.matcom.2019.04.009
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    References listed on IDEAS

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    5. Marcos Escobar & Peter Hieber & Matthias Scherer, 2014. "Efficiently pricing double barrier derivatives in stochastic volatility models," Review of Derivatives Research, Springer, vol. 17(2), pages 191-216, July.
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    Citations

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    Cited by:

    1. Gao, Yin & Jia, Lifen, 2021. "Pricing formulas of barrier-lookback option in uncertain financial markets," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    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. Jin, Ting & Ding, Hui & Xia, Hongxuan & Bao, Jinfeng, 2021. "Reliability index and Asian barrier option pricing formulas of the uncertain fractional first-hitting time model with Caputo type," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    4. Liu, Hanjie & Zhu, Yuanguo, 2024. "Carbon option pricing based on uncertain fractional differential equation: A binomial tree approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 13-28.
    5. Jin, Ting & Zhu, Yuanguo, 2020. "First hitting time about solution for an uncertain fractional differential equation and application to an uncertain risk index model," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    6. Jian Zhou & Yujiao Jiang & Athanasios A. Pantelous & Weiwen Dai, 2023. "A systematic review of uncertainty theory with the use of scientometrical method," Fuzzy Optimization and Decision Making, Springer, vol. 22(3), pages 463-518, September.
    7. 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).
    8. Yu, Yongjiu & Yang, Xiangfeng & Lei, Qing, 2022. "Pricing of equity swaps in uncertain financial market," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    9. Carlos Esparcia & Elena Ibañez & Francisco Jareño, 2020. "Volatility Timing: Pricing Barrier Options on DAX XETRA Index," Mathematics, MDPI, vol. 8(5), pages 1-25, May.
    10. Kai Yao & Zhongfeng Qin, 2021. "Barrier option pricing formulas of an uncertain stock model," Fuzzy Optimization and Decision Making, Springer, vol. 20(1), pages 81-100, March.
    11. Pan, Zeyu & Gao, Yin & Yuan, Lin, 2021. "Bermudan options pricing formulas in uncertain financial markets," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    12. Jia, Lifen & Liu, Xueyong, 2021. "Optimal harvesting strategy based on uncertain logistic population model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    13. Jin, Ting & Yang, Xiangfeng, 2021. "Monotonicity theorem for the uncertain fractional differential equation and application to uncertain financial market," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 203-221.
    14. Gao, Rong & Wu, Wei & Lang, Chao & Lang, Liying, 2020. "Geometric Asian barrier option pricing formulas of uncertain stock model," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

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