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Critical Value-Based Power Options Pricing Problems in Uncertain Financial Markets

Guimin Yang

School of Science, Nanjing University of Science and Technology, P. R. China, Nanjing 210094, Jiangsu, P. R. China

E-mail Address: Yanggm@njust.edu.cn

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and

Yuanguo Zhu

School of Science, Nanjing University of Science and Technology, P. R. China, Nanjing 210094, Jiangsu, P. R. China

E-mail Address: ygzhu@njust.edu.cn

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https://doi.org/10.1142/S1752890921500021Cited by:6 (Source: Crossref)

Abstract

Compared with investing an ordinary options, investing the power options may possibly yield greater returns. On the one hand, the power option is the best choice for those who want to maximize the leverage of the underlying market movements. On the other hand, power options can also prevent the financial market changes caused by the sharp fluctuations of the underlying assets. In this paper, we investigate the power option pricing problem in which the price of the underlying asset follows the Ornstein–Uhlenbeck type of model involving an uncertain fractional differential equation. Based on critical value criterion, the pricing formulas of European power options are derived. Finally, some numerical experiments are performed to illustrate the results.

Keywords:

References

1. F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Politic. Econ. 81(3) (1973) 637–654. Crossref, Google Scholar
2. R. C. Merton, Theory of rational option pricing, Bell J. Econ. Management Sci. 4 (1973) 141–183. Crossref, Google Scholar
3. B. Liu, Uncertainty Theory (Springer-Verlag, Berlin, 2007). Crossref, Google Scholar
4. B. Liu, Some research problems in uncertainty theory, J. Uncertain Syst. 3(1) (2009) 3–10. Google Scholar
5. Z. Zhang, W. Liu and Y. Sheng, Valuation of power option for uncertain financial market, Appl. Math. Comput. 286 (2016) 257–264. Google Scholar
6. Y. Sun, K. Yao and Z. Fu, Interest rate model in uncertain environment based on exponential Ornstein–Uhlenbeck equation, Soft Comput. 22 (2018) 465–475. Crossref, Google Scholar
7. Y. Zhu, Uncertain fractional differential equations and an interest rate model, Math. Methods Appl. Sci. 38(15) (2015) 3359–3368. Crossref, Google Scholar
8. Z. Lu, Y. Zhu and B. Li, Critial value-based Asian option pricing model for uncertain financial markets, Phys. A 525 (2019) 694–703. Crossref, Google Scholar
9. Z. Lu and Y. Zhu, Numerical approach for solution to an uncertain fractional differential equation, Appl. Math. Comput. 343 (2019) 137–148. Crossref, Google Scholar
10. J. Peng and K. Yao, A new option pricing model for stocks in uncertainty markets, Int. J. Oper. Res. 8(2) (2011) 18–26. Google Scholar
11. L. Dai, Z. Fu and Z. Huang, Option pricing formulas for uncertain financial market based on the exponential Ornstein–Uhlenbeck model, J. Intell. Manufact. 28 (2017) 597–604. Crossref, Google Scholar
12. G. Yang and Y. Zhu, Expected value-based power options pricing under uncertain circumstance, Int. Math. Forum. 15(8) (2020) 369–376. Crossref, Google Scholar
13. L. Sheng, Y. Zhu and K. Wang, Analysis of a class of dynamic programming models for multi-stage uncertain systems, Appl. Math. Mod. 86 (2020) 446–459. Crossref, Google Scholar
14. L. Sheng, Y. Zhu and K. Wang, Uncertain dynamical systems-based decision making with application to production-inventory problems, Appl. Math. Mod. 56 (2018) 275–288. Crossref, Google Scholar
15. K. Diethelm, N. J. Ford and A. D. Freed, A predictor-corrector approach for the numerical solution of fractional differential equations, Nonlinear Dynam. 29 (2002) 3–22. Crossref, Google Scholar