Skip to main content
SpringerLink
Log in

European Option Pricing Under Fuzzy CEV Model

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

In modern financial market, option is a very effective tool to hedge the risks brought by various uncertainties in real society. Therefore, it is of great significance to select an appropriate stock model to price options. To this aim, the paper presents a general stock model with fuzzy volatility for fuzzy financial market, that is, fuzzy constant elasticity of variance model. The advantage is that the fuzzy volatility of underlying stock is related to its price and can explain volatility smile. In addition, we consider the impact of elasticity coefficient on stock price and then limit the elasticity coefficient to a reasonable range. Subsequently, the European call and European put option pricing formulas are given, separately. Finally, some figures and tables are given to illustrate the impact of parameter changes on option prices.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Araneda, A., Villena, M.: Computing the CEV option pricing formula using the semiclassical approximation of path integral. J. Comput. Appl. Math. 388, 113244 (2021)

  2. Bian, L., Li, Z.: Fuzzy simulation of European option pricing using sub-fractional Brownian motion. Chaos, Solitons Fractals 153, 111442 (2021)

    MathSciNet  Google Scholar 

  3. Black, F., Scholes, M.: The pricing of option and corporate liabilities. J. Polit. Econ. 81, 637–654 (1973)

    MathSciNet  MATH  Google Scholar 

  4. Chen, X., Qin, Z.: A new existence and unqueness theorem for fuzzy differential equation. Int. J. Fuzzy Syst. 13(2), 148–151 (2011)

    MathSciNet  Google Scholar 

  5. Cheng, Y., You, C.: Convergence of numerical methods for fuzzy differential equations. J. Intell. Fuzzy Syst. 38(4), 5257–5266 (2020)

    Google Scholar 

  6. Cox, J., Ross, S.: The valuation of options for alternative stochastic processes. J. Financ. Econ. 4, 145–166 (1976)

    Google Scholar 

  7. Cox, J., Ingersoll, J., Ross, S.: An intertemporal general equilibrium model of asset prices. Economentrica 53, 145–153 (1989)

    MATH  Google Scholar 

  8. Cruz, A., Dias, J.: Valuing American-style options under the CEV model: an integral representation based method. Rev. Deriv. Res. 23, 63–83 (2020)

    MATH  Google Scholar 

  9. Gao, J.: Credibilistic option pricing: a new model. J. Uncertain Syst. 2(4), 243–247 (2008)

    Google Scholar 

  10. Gu, A., Guo, X., Li, Z., et al.: Optimal control of excess-of-loss reinsurance and investment for insurers under a CEV model. Insurance Math. Econ. 51(3), 674–684 (2012)

    MathSciNet  MATH  Google Scholar 

  11. Lee, J.: An efficient numerical method for pricing American put options under the CEV model. J. Comput. Appl. Math. 389(3), 113311 (2020)

    MathSciNet  MATH  Google Scholar 

  12. Liu, B., Liu, Y.: Expected value of fuzzy variable and fuzzy expected value models. IEEE Trans. Fuzzy Syst. 10(4), 445–450 (2002)

    Google Scholar 

  13. Liu, B.: Uncertainty Theory: An Introduction to its Axiomatic Foundations. Springer-Verlag, Berlin (2004)

    MATH  Google Scholar 

  14. Liu, B.: Uncertainty Theory, 2nd edn. Springer-Verlag, Berlin (2007)

    MATH  Google Scholar 

  15. Liu, B.: Fuzzy process, hybrid process and uncertain process. J. Uncertain Syst. 2(1), 3–16 (2008)

    Google Scholar 

  16. Liu, Y.: An analytic method for solving uncertain differential differential equations. J. Uncertain Syst. 6(4), 244–249 (2012)

    Google Scholar 

  17. Liu, W., Li, S.: European option pricing model in a stochastic and fuzzy environment. Appl. Math. A J. Chinese Univ. 28(3), 321–334 (2013)

    MathSciNet  MATH  Google Scholar 

  18. Li, H., Ware, A., Di, L., et al.: The application of nonlinear fuzzy parameters PDE method in pricing and hedging Europeam options. Fuzzy Sets Syst. 331, 14–25 (2018)

    MATH  Google Scholar 

  19. Ma, J., Lu, Z., et al.: Least-squares Monte-Carlo methods for optimal stoppong investment under CEV models. Quant. Finan. 20(7), 1199–1211 (2020)

    MATH  Google Scholar 

  20. Mao, L., Zhang, Y.: Robust optimal excess-of-loss reinsurance and investment problem with \(p\)-thinning dependent risks under CEV model. Quant. Finance Econom. 5(1), 134–162 (2021)

    Google Scholar 

  21. Peng, J.: A general stock model for fuzzy markets. J. Uncertain Syst. 2(4), 248–254 (2008)

    Google Scholar 

  22. Qin, Z., Liu, B.: Option pricing formula for fuzzy financial market. J. Uncertain Syst. 2(1), 17–21 (2008)

    Google Scholar 

  23. Qin, Z., Gao, X.: Fracrional Liu process with application to finance. Math. Comput. Model. 50(9–10), 1538–1543 (2009)

    MATH  Google Scholar 

  24. You, C., Wang, W., Huo, H.: Existence and uniqueness theorems for fuzzy differential equations. J. Uncertain Syst. 7(4), 303–315 (2013)

    Google Scholar 

  25. You, C., Hao, Y.: Fuzzy Euler approximation and its local convergence. J. Comput. Appl. Math. 343(2018), 55–61 (2018)

    MathSciNet  MATH  Google Scholar 

  26. You, C., Hao, Y.: Numerical solution of fuzzy differential equation based on Taylor expansion. J. Hebei Univ. (Nature Science) 38(2), 113–118 (2018)

    Google Scholar 

  27. You, C., Bo, L.: Option pricing formulas for generalized fuzzy stock model. J. Indus. Manag. Optim. 16(1), 387–396 (2020)

    MathSciNet  MATH  Google Scholar 

  28. You, C., Bo, L.: Option pricing based on a type of fuzzy process. J. Ambient. Intell. Humaniz. Comput. 13(8), 3771–3785 (2022)

    Google Scholar 

  29. Zadeh, L.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)

    MATH  Google Scholar 

  30. Zadeh, L.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1, 3–28 (1978)

    MathSciNet  MATH  Google Scholar 

  31. Zhang, Y., You, C.: Option pricing formula for a new stock model. Adv. Appl. Math. 7(10), 1225–1232 (2018)

    Google Scholar 

Download references

Acknowledgements

This work was supported by Science and Technology Project of Hebei Education Department Nos. ZD2020172 and QN2020124.

Author information

Authors and Affiliations

  1. College of Mathematics and Information Science, Hebei University, Baoding, 071002, China

    Xinyue Wei, Cuilian You & Yujie Zhang

  2. Hebei Key Lab of Machine Learning and Computation Intelligence, Hebei University, Baoding, 071002, China

    Cuilian You

Authors
  1. Xinyue Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cuilian You
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yujie Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cuilian You.

Additional information

Communicated by Kok Lay Teo.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wei, X., You, C. & Zhang, Y. European Option Pricing Under Fuzzy CEV Model. J Optim Theory Appl 196, 415–432 (2023). https://doi.org/10.1007/s10957-022-02108-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-022-02108-w

Keywords

Search

Navigation