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JACIII Vol.26 No.6 pp. 1031-1039
doi: 10.20965/jaciii.2022.p1031
(2022)

Paper:

Option Pricing for Uncertain Stock Model Based on Optimistic Value

Liubao Deng*,**,†, Hongye Tan*, Fang Wei*, and Yilin Wang*

*School of Business, Guangzhou College of Technology and Business
No.5 Guangming Road, Haibu, Shiling Town, Huadu District, Guangzhou City, Guangdong 510850, China

**School of Finance, Anhui University of Finance and Economics
Bengbu 233030, China

Corresponding author

Received:
May 19, 2022
Accepted:
July 25, 2022
Published:
November 20, 2022
Keywords:
option pricing, optimistic value, uncertainty
Abstract

Option pricing plays an important role in modern finance. This paper investigates the uncertain option pricing problems based on uncertainty theory by using the method to calculate the optimistic value of uncertain returns of options instead of the method of traditional expected value in the sense of the weighted average. The pricing formulas of the European and American options are derived for Liu’s uncertain stock model and Peng’s mean-reverting stock model which are two basic and representative uncertain stock models in uncertain finance. In the end, some numerical experiments are given to illustrate the effectiveness of the obtained results.

Cite this article as:
L. Deng, H. Tan, F. Wei, and Y. Wang, “Option Pricing for Uncertain Stock Model Based on Optimistic Value,” J. Adv. Comput. Intell. Intell. Inform., Vol.26, No.6, pp. 1031-1039, 2022.
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References
  1. [1] F. Black and M. Scholes, “The pricing of option and corporate liabilities,” J. Polit. Econ., Vol.81, No.3, pp. 637-654, 1973.
  2. [2] B. Liu, “Why is there a need for uncertainty theory?,” J. of Uncertain Systems, Vol.6, No.1, pp. 3-10, 2012.
  3. [3] B. Liu, “Uncertainty Theory (2nd Ed.),” Springer Berlin, Heidelberg, 2007.
  4. [4] B. Liu, “Fuzzy process, hybrid process and uncertain process,” J. of Uncertain Systems, Vol.2, No.1, pp. 3-16, 2008.
  5. [5] B. Liu, “Some research problems in uncertainty theory,” J. of Uncertain Systems, Vol.3, No.1, pp. 3-10, 2009.
  6. [6] B. Li, Y. Zhu, Y. Sun, A. Grace, and K. Teo, “Multi-period portfolio selection problem under uncertain environment with bankruptcy constraint,” Appl. Math. Model., Vol.56, pp. 539-550, 2018.
  7. [7] X. Chen, “American option pricing formula for uncertain financial market,” Int. J. Oper. Res., Vol.8, No.2, pp. 27-32, 2011.
  8. [8] B. Liu, “Uncertain risk analysis and uncertain reliability analysis,” J. of Uncertain Systems, Vol.4, No.3, pp. 163-170, 2010.
  9. [9] K. Yao and J. Zhou, “Ruin time of uncertain insurance risk process,” IEEE Trans. Fuzzy Syst., Vol.26, No.1, pp. 19-28, 2018.
  10. [10] X. Wang, Z. Gao, and H. Guo, “Uncertain hypothesis testing for two experts’ empirical data,” Math. Comput. Model., Vol.55, Nos.3-4, pp. 1478-1482, 2012.
  11. [11] Z. Zou, B. Jiang, J. Li, and W. Lio, “Uncertain Weibull regression model with imprecise observations,” Soft Computing, Vol.25, pp. 2767-2775, 2021.
  12. [12] B. Liu, “Theory and Practice of Uncertain Programming (2nd Ed.),” Springer Berlin, Heidelberg, 2009.
  13. [13] Z. Wang, J. Guo, M. Zheng, and Y. Wang, “Uncertain multiobjective traveling salesman problem,” European J. of Operational Research, Vol.241, No.2, pp. 478-489, 2015.
  14. [14] L. Deng and Y. Chen, “Optimistic value model of uncertain linear quadratic optimal control with jump,” J. Adv. Comput. Intell. Intell. Inform., Vol.20, No.2, pp. 189-196, 2016.
  15. [15] Y. Chen and L. Deng, “Discrete-Time Uncertain LQ Optimal Control with Indefinite Control Weight Costs,” J. Adv. Comput. Intell. Intell. Inform., Vol.20, No.4, pp. 633-639, 2016.
  16. [16] B. Liu, “Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty,” Springer Berlin, Heidelberg, 2010.
  17. [17] J. Sun and X. Chen, “Asian option pricing formula for uncertain financial market,” J. Uncertain. Anal. Appl., Vol.3, Article No.11, 2015.
  18. [18] Z. Zhang and W. Liu, “Geometric average Asian option pricing for uncertain financial market,” J. Uncertain Syst., Vol.8, No.4, pp. 317-320, 2014.
  19. [19] Y. Gao, X. Yang, and Z. Fu, “Lookback option pricing problem of uncertain exponential Ornstein–Uhlenbeck model,” Soft Comput., Vol.22, pp. 5647-5654, 2018.
  20. [20] Z. Liu, “Lookback option pricing problems of uncertain mean-reverting stock model,” J. Adv. Comput. Intell. Intell. Inform., Vol.25, No.5, pp. 539-545, 2021.
  21. [21] R. Gao, K. Liu, Z. Li, and R. Lv, “American barrier option pricing formulas for stock model in uncertain environment,” IEEE Access, Vol.7, pp. 97846-97856, 2019.
  22. [22] Z. Zhang, W. Liu, and Y. Sheng, “Valuation of power option for uncertain financial market,” Appl. Math. Comput., Vol.286, pp. 257-264, 2016.
  23. [23] Z. Zhang, D. A. Ralescu, and W. Liu, “Valuation of interest rate ceiling and floor in uncertain financial market,” Fuzzy Optimization and Decision Making, Vol.15, pp. 139-154, 2016.
  24. [24] Y. Liu, X. Chen, and D. A. Ralescu, “Uncertain currency model and currency option pricing,” Int. J. of Intelligent Systems, Vol.30, No.1, pp. 40-51, 2015.
  25. [25] J. Peng and K. Yao, “A new option pricing model for stocks in uncertainty markets,” Int. J. of Operations Research, Vol.8, No.2, pp. 18-26, 2011.
  26. [26] Y. Shen and K. Yao, “A mean-reverting currency model in an uncertain environment,” Soft Comput., Vol.20, pp. 4131-4138, 2016.
  27. [27] X. Wang and Y. Ning, “An uncertain currency model with floating interest rates,” Soft Comput., No.21, pp. 6739-6754, 2017.
  28. [28] X. Ji and J. Zhou, “Option pricing for an uncertain stock model with jumps,” Soft Comput., Vol.19, pp. 3323-3329, 2015.
  29. [29] F. Black and P. Karasinski, “Bond and option pricing when short-term rates are lognormal,” Financial Analysts J., Vol.47, No.4, pp. 52-59, 1991.

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Last updated on Dec. 01, 2022