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Critical value-based Asian option pricing model for uncertain financial markets

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  • Lu, Ziqiang
  • Zhu, Yuanguo
  • Li, Bo

Abstract

Asian option has become one of the most popular financial derivatives in the OTC (Over-the-Counter) market due to its low risk and cost. The option pricing problem which regards the price of the underlying asset as a random variable has been extensively studied based on the sufficient historical data. It may be modeled as an uncertain variable when the historical data is lack. This paper investigates the Asian option pricing problem based on uncertainty theory, in which the price of the underlying asset follows the mean-reverting process involving an uncertain fractional differential equation. The pricing formulas of the Asian options are derived based on the expected value and optimistic value. Some numerical experiments are performed to illustrate the results.

Suggested Citation

  • Lu, Ziqiang & Zhu, Yuanguo & Li, Bo, 2019. "Critical value-based Asian option pricing model for uncertain financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 694-703.
    • Handle: RePEc:eee:phsmap:v:525:y:2019:i:c:p:694-703
    DOI: 10.1016/j.physa.2019.04.022
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    1. Corwin Joy & Phelim P. Boyle & Ken Seng Tan, 1996. "Quasi-Monte Carlo Methods in Numerical Finance," Management Science, INFORMS, vol. 42(6), pages 926-938, June.
    2. Yiyao Sun & Taoyong Su, 2017. "Mean-reverting stock model with floating interest rate in uncertain environment," Fuzzy Optimization and Decision Making, Springer, vol. 16(2), pages 235-255, June.
    3. Kemna, A. G. Z. & Vorst, A. C. F., 1990. "A pricing method for options based on average asset values," Journal of Banking & Finance, Elsevier, vol. 14(1), pages 113-129, March.
    4. Zhang, Wei-Guo & Li, Zhe & Liu, Yong-Jun, 2018. "Analytical pricing of geometric Asian power options on an underlying driven by a mixed fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 402-418.
    5. Luo, Ming & Wu, Shaomin, 2018. "A value-at-risk approach to optimisation of warranty policy," European Journal of Operational Research, Elsevier, vol. 267(2), pages 513-522.
    6. Jin E. Zhang, 2003. "Pricing continuously sampled Asian options with perturbation method," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 23(6), pages 535-560, June.
    7. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May.
    8. Ghafarian, Bahareh & Hanafizadeh, Payam & Qahi, Amir Hossein Mortazavi, 2018. "Applying Greek letters to robust option price modeling by binomial-tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 632-639.
    9. Yoshida, Yuji, 2003. "The valuation of European options in uncertain environment," European Journal of Operational Research, Elsevier, vol. 145(1), pages 221-229, February.
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    Cited by:

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    3. Lu, Qinyun & Zhu, Yuanguo, 2021. "LQ optimal control of fractional-order discrete-time uncertain systems," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    4. Lingling Xu & Hongjie Zhang & Fu Lee Wang, 2023. "Pricing of Arithmetic Average Asian Option by Combining Variance Reduction and Quasi-Monte Carlo Method," Mathematics, MDPI, vol. 11(3), pages 1-14, January.
    5. Zhu, Kai & Ji, Kaiyuan & Shen, Jiayu, 2021. "A fixed charge transportation problem with damageable items under uncertain environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    6. Liu, Yiyu & Zhu, Yuanguo & Lu, Ziqiang, 2021. "On Caputo-Hadamard uncertain fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    7. Dastranj, Elham & Sahebi Fard, Hossein & Abdolbaghi, Abdolmajid & Reza Hejazi, S., 2020. "Power option pricing under the unstable conditions (Evidence of power option pricing under fractional Heston model in the Iran gold market)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    8. Weiwei Wang & Dan A. Ralescu, 2021. "Option pricing formulas based on uncertain fractional differential equation," Fuzzy Optimization and Decision Making, Springer, vol. 20(4), pages 471-495, December.
    9. Liu He & Yuanguo Zhu & Ziqiang Lu, 2023. "Parameter estimation for uncertain fractional differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 22(1), pages 103-122, March.
    10. 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).
    11. 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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