Advertisement

Soft Computing

, Volume 22, Issue 17, pp 5583–5592 | Cite as

Asian option pricing problems of uncertain mean-reverting stock model

  • Yiyao Sun
  • Kai Yao
  • Jichang Dong
Focus

Abstract

An Asian option is a special type of option contract which reduces the volatility inherent in the option because of the averaging feature, so it is one of the most actively exotic options traded in today’s financial derivative market. As an application of the uncertain process in the field of finance, the uncertain finance assumes that the asset price follows an uncertain differential equation. In this paper, Asian options are proposed in the uncertain financial market based on a mean-reverting stock model and their pricing formulas are derived. In addition, some numerical algorithms are designed to compute the prices of the Asian options on the basis of the pricing formulas.

Keywords

Uncertainty theory Uncertain differential equation Stock model Asian option 

Notes

Acknowledgements

This study was funded by the National Natural Science Foundation of China (Grant Nos. 61403360, 71532013 and 71573244) and the Open Project of Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

Clarification

This work was carried out in collaboration between all authors. All authors read and approved the final manuscript.

References

  1. Bachelier L (1900) Théorie de la spéculation. Ann Sci L École Normale Supérieure 3(17):21–86CrossRefMATHGoogle Scholar
  2. Black F, Scholes M (1973) The pricing of options and corporate liabilities. J Polit Econ 81:637–654MathSciNetCrossRefMATHGoogle Scholar
  3. Carverhill A, Clewlow L (1990) Flexible convolution. In: From Black Scholes to Black Holes, Risk Books, London pp 165–171Google Scholar
  4. Chen X (2011) American option pricing formula for uncertain financial market. Int J Oper Res 8(2):32–37MathSciNetGoogle Scholar
  5. Chen X, Liu B (2010) Existence and uniqueness theorem for uncertain differential equations. Fuzzy Optim Decis Mak 9(1):69–81MathSciNetCrossRefMATHGoogle Scholar
  6. Chen X, Liu Y, Ralescu DA (2013) Uncertain stock model with periodic dividends. Fuzzy Optim Decis Mak 12(1):111–123MathSciNetCrossRefGoogle Scholar
  7. Gao JW (2013) Uncertain bimatrix game with applications. Fuzzy Optim Decis Mak 12(1):65–78MathSciNetCrossRefGoogle Scholar
  8. Gao JW, Yang XF, Liu D (2017) Uncertain shapley value of coalitional game with application to supply chain alliance. Appl Soft Comput. doi: 10.1016/j.asoc.2016.06.018 Google Scholar
  9. Guo C, Gao JW (2017) Optimal dealer pricing under transaction uncertainty. J Intell Manuf. doi: 10.1007/s10845-014-1002-8 Google Scholar
  10. Ji XY, Zhou J (2015) Option pricing for an uncertain stock model with jumps. Soft Comput 19(11):3323–3329CrossRefMATHGoogle Scholar
  11. Kemna A, Vorst A (1990) A pricing method for options based on average asset values. J Bank Financ 14:113–129CrossRefGoogle Scholar
  12. Liu B (2007) Uncertain Theory, 2nd edn. Springer, BerlinGoogle Scholar
  13. Liu B (2008) Fuzzy process, hybrid process and uncertain process. J Uncertain Syst 2(1):3–16Google Scholar
  14. Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10Google Scholar
  15. Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, BerlinCrossRefGoogle Scholar
  16. Ni YD (2017) Sequential seeding to optimize influence diffusion in a social network. Appl Soft Comput. doi: 10.1016/j.asoc.2016.04.025 Google Scholar
  17. Ni YD, Zhao ZJ (2017) Two-agent scheduling problem under fuzzy environment. J Intell Manuf 28(3):739–748Google Scholar
  18. Ni YD, Ning L, Ke H, Ji XY (2017) Modeling and minimizing information distortion in information diffusion through a social network. Soft Comput. doi: 10.1007/s00500-016-2277-9 Google Scholar
  19. Rogers L, Shi Z (1995) The value of an Asian option. J Appl Probab 32:1077–1088MathSciNetCrossRefMATHGoogle Scholar
  20. Shen JY, Zhu YG (2016) Chance-constrained model for uncertain job shop scheduling problem. Soft Comput 20(6):2383–2391CrossRefMATHGoogle Scholar
  21. Sun JJ, Chen XW (2015) Asian option pricing formula for uncertain financial market. J Uncertain Anal Appl 3:11CrossRefGoogle Scholar
  22. Sun YY, Su TY (2016) Mean-reverting stock model with floating interest rate in uncertain environment. Fuzzy Optim Decis Mak. doi: 10.1007/s10700-016-9247-7 Google Scholar
  23. Wiener N (1923) Differential space. J Math Phys 2(1):131–174CrossRefGoogle Scholar
  24. Yang XF, Gao JW (2016) Linear quadratic uncertain differential game with application to resource extraction problem. IEEE Trans Fuzzy Syst 24(4):819–826CrossRefGoogle Scholar
  25. Yang XF, Gao JW (2017) Bayesian equilibria for uncertain bimatrix game with asymmetric information. J Intell Manuf. doi: 10.1007/s10845-014-1010-8 Google Scholar
  26. Yao K (2013) Extreme values and integral of solution of uncertain differential equations. J Uncertain Anal Appl 1:2CrossRefGoogle Scholar
  27. Yao K (2015) Uncertain contour process and its application in stock model with floating interest rate. Fuzzy Optim Decis Mak 14(4):399–424MathSciNetCrossRefGoogle Scholar
  28. Yao K, Chen X (2013) A numerical method for solving uncertain differential equations. J Intell Fuzzy Syst 25(3):825–832MathSciNetMATHGoogle Scholar
  29. Zhang ZQ, Liu WQ (2014) Geometric average Asian option pricing for uncertain financial market. J Uncertain Syst 8(4):317–320Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of Economics and ManagementUniversity of Chinese Academy of SciencesBeijingChina
  2. 2.Key Laboratory of Big Data Mining and Knowledge ManagementChinese Academy of SciencesBeijingChina

Personalised recommendations