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Reliability index and Asian barrier option pricing formulas of the uncertain fractional first-hitting time model with Caputo type

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  • Jin, Ting
  • Ding, Hui
  • Xia, Hongxuan
  • Bao, Jinfeng

Abstract

This paper mainly studies the pricing problem of arithmetic average Asian barrier options in the continuous case and analyzes the corresponding reliability index. Owing to the fact that the return function of the option is closely related to the average price of the underlying asset in a certain period, which can effectively alleviate the market speculation, the Asian barrier option is widely active in the financial market as a derivative product. Firstly, considering that there exists difficult to predict and measure reliability based on historical data, traditional stock models relied on stochastic theory are abandoned, and further assumes that the underlying assets follow an uncertain process. Then, we introduce the uncertain fractional differential equations with Caputo-type to describe the dynamic changes of risky asset prices. Secondly, in order to analyze the impact on the first hitting time of the barrier being triggered and the option execution result theoretically, a novel first-hitting time model is established to measure the relationship between the option reliability index and the value of risky assets. Meanwhile, the pricing formulas of four Asian barrier options and the corresponding reliability index under the first-hitting time model are derived, respectively. Finally, numerical algorithms and corresponding methods are designed to verify the results of our model.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:142:y:2021:i:c:s096007792030802x
    DOI: 10.1016/j.chaos.2020.110409
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    1. Hu, Lunhu & Kang, Rui & Pan, Xing & Zuo, Dujun, 2020. "Risk assessment of uncertain random system—Level-1 and level-2 joint propagation of uncertainty and probability in fault tree analysis," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    2. Dickson,David C. M., 2016. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9781107154605, January.
    3. Lu, Ziqiang & Zhu, Yuanguo, 2019. "Numerical approach for solution to an uncertain fractional differential equation," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 137-148.
    4. 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.
    5. Wu, Ji-Peng & Kang, Rui & Li, Xiao-Yang, 2020. "Uncertain accelerated degradation modeling and analysis considering epistemic uncertainties in time and unit dimension," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    6. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    7. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    8. Tian, Miao & Yang, Xiangfeng & Kar, Samarjit, 2019. "Equity warrants pricing problem of mean-reverting model in uncertain environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
    9. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-367, May.
    10. Jin, Ting & Sun, Yun & Zhu, Yuanguo, 2019. "Extreme values for solution to uncertain fractional differential equation and application to American option pricing model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    11. Fusai, Gianluca & Recchioni, Maria Cristina, 2007. "Analysis of quadrature methods for pricing discrete barrier options," Journal of Economic Dynamics and Control, Elsevier, vol. 31(3), pages 826-860, March.
    12. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    13. 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).
    14. Ziqiang Lu & Hongyan Yan & Yuanguo Zhu, 2019. "European option pricing model based on uncertain fractional differential equation," Fuzzy Optimization and Decision Making, Springer, vol. 18(2), pages 199-217, June.
    15. 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.
    16. 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.
    17. Mark Broadie & Paul Glasserman & Steven Kou, 1997. "A Continuity Correction for Discrete Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 325-349, October.
    18. Jin, Ting & Sun, Yun & Zhu, Yuanguo, 2020. "Time integral about solution of an uncertain fractional order differential equation and application to zero-coupon bond model," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    19. 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).
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    1. Wang, Weiwei & Ralescu, Dan A., 2021. "Valuation of lookback option under uncertain volatility model," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).

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