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Asian-barrier option pricing formulas of uncertain financial market

Author

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  • Yang, Xiangfeng
  • Zhang, Zhiqiang
  • Gao, Xin

Abstract

Barrier option is an exotic option on an underlying asset whose payoff depends on whether or not the underlying asset’s price has reached predetermined barrier level. This paper mainly investigates Asian-barrier option pricing problem under uncertain financial market. Assume that stock price follows an uncertain differential equation, some Asian-barrier option pricing formulas are derived. Moreover, several numerical examples are given to illustrate the effectiveness of the proposed model.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:123:y:2019:i:c:p:79-86
    DOI: 10.1016/j.chaos.2019.03.037
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    References listed on IDEAS

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    1. Lanruo Dai & Zongfei Fu & Zhiyong Huang, 2017. "Option pricing formulas for uncertain financial market based on the exponential Ornstein–Uhlenbeck model," Journal of Intelligent Manufacturing, Springer, vol. 28(3), pages 597-604, March.
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    4. 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.
    5. Ballestra, Luca Vincenzo & Pacelli, Graziella & Radi, Davide, 2016. "A very efficient approach for pricing barrier options on an underlying described by the mixed fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 240-248.
    6. Lee, Min-Ku, 2016. "Asymptotic approach to the pricing of geometric asian options under the CEV model," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 544-548.
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    Citations

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    Cited by:

    1. Wang, Weiwei & Ralescu, Dan A., 2021. "Valuation of lookback option under uncertain volatility model," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    2. 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.
    3. Gao, Yin & Gao, Jinwu & Yang, Xiangfeng, 2022. "The almost sure stability for uncertain delay differential equations based on normal lipschitz conditions," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    4. Sheng, Yuhong & Yao, Kai & Qin, Zhongfeng, 2020. "Continuity and variation analysis of fractional uncertain processes," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. 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).
    6. 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).
    7. Deng, Jie & Qin, Zhongfeng, 2021. "On Parisian option pricing for uncertain currency model," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    8. 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.
    9. Liu, Yang & Lio, Waichon, 2024. "Power option pricing problem of uncertain exponential Ornstein–Uhlenbeck model," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    10. Jia, Lifen & Chen, Wei, 2020. "Knock-in options of an uncertain stock model with floating interest rate," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    11. 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).
    12. Gao, Yin & Jia, Lifen, 2021. "Pricing formulas of barrier-lookback option in uncertain financial markets," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    13. Pan, Zeyu & Gao, Yin & Yuan, Lin, 2021. "Bermudan options pricing formulas in uncertain financial markets," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    14. 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).
    15. 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).
    16. Gao, Yin & Tian, Miao, 2024. "Pricing problem and sensitivity analysis of knock-in external barrier options based on uncertain stock model," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    17. Shi, Gang & Gao, Jinwu, 2021. "European Option Pricing Problems with Fractional Uncertain Processes," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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