IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v196y2023i2d10.1007_s10957-022-02108-w.html
   My bibliography  Save this article

European Option Pricing Under Fuzzy CEV Model

Author

Listed:
  • Xinyue Wei

    (Hebei University)

  • Cuilian You

    (Hebei University
    Hebei University)

  • Yujie Zhang

    (Hebei University)

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.

Suggested Citation

  • Xinyue Wei & Cuilian You & Yujie Zhang, 2023. "European Option Pricing Under Fuzzy CEV Model," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 415-432, February.
  • Handle: RePEc:spr:joptap:v:196:y:2023:i:2:d:10.1007_s10957-022-02108-w
    DOI: 10.1007/s10957-022-02108-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-022-02108-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10957-022-02108-w?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Lee, Jung-Kyung, 2020. "A simple numerical method for pricing American power put options," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Gu, Ailing & Guo, Xianping & Li, Zhongfei & Zeng, Yan, 2012. "Optimal control of excess-of-loss reinsurance and investment for insurers under a CEV model," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 674-684.
    3. Jingtang Ma & Zhengyang Lu & Wenyuan Li & Jie Xing, 2020. "Least-squares Monte-Carlo methods for optimal stopping investment under CEV models," Quantitative Finance, Taylor & Francis Journals, vol. 20(7), pages 1199-1211, July.
    4. Bian, Liu & Li, Zhi, 2021. "Fuzzy simulation of European option pricing using sub-fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    5. Aricson Cruz & José Carlos Dias, 2020. "Valuing American-style options under the CEV model: an integral representation based method," Review of Derivatives Research, Springer, vol. 23(1), pages 63-83, April.
    6. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chinonso Nwankwo & Weizhong Dai & Tony Ware, 2023. "Enhancing accuracy for solving American CEV model with high-order compact scheme and adaptive time stepping," Papers 2309.03984, arXiv.org, revised Sep 2023.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Josa-Fombellida, Ricardo & López-Casado, Paula & Rincón-Zapatero, Juan Pablo, 2018. "Portfolio optimization in a defined benefit pension plan where the risky assets are processes with constant elasticity of variance," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 73-86.
    2. Peter Carr & Liuren Wu, 2014. "Static Hedging of Standard Options," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 3-46.
    3. Sergio Zúñiga, 1999. "Modelos de Tasas de Interés en Chile: Una Revisión," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 36(108), pages 875-893.
    4. Sandrine Lardic & Claire Gauthier, 2003. "Un modèle multifactoriel des spreads de crédit : estimation sur panels complets et incomplets," Économie et Prévision, Programme National Persée, vol. 159(3), pages 53-69.
    5. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.
    6. Bettis, J. Carr & Bizjak, John & Coles, Jeffrey L. & Kalpathy, Swaminathan, 2018. "Performance-vesting provisions in executive compensation," Journal of Accounting and Economics, Elsevier, vol. 66(1), pages 194-221.
    7. Hi Jun Choe & Jeong Ho Chu & So Jeong Shin, 2014. "Recombining binomial tree for constant elasticity of variance process," Papers 1410.5955, arXiv.org.
    8. Rodriguez, Ricardo J., 2002. "Lognormal option pricing for arbitrary underlying assets: a synthesis," The Quarterly Review of Economics and Finance, Elsevier, vol. 42(3), pages 577-586.
    9. Monteiro, Ana Margarida & Tutuncu, Reha H. & Vicente, Luis N., 2008. "Recovering risk-neutral probability density functions from options prices using cubic splines and ensuring nonnegativity," European Journal of Operational Research, Elsevier, vol. 187(2), pages 525-542, June.
    10. Shuang Xiao & Guo Li & Yunjing Jia, 2017. "Estimating the Constant Elasticity of Variance Model with Data-Driven Markov Chain Monte Carlo Methods," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(01), pages 1-23, February.
    11. Andrea Pascucci & Marco Di Francesco, 2005. "On the complete model with stochastic volatility by Hobson and Rogers," Finance 0503013, University Library of Munich, Germany.
    12. Chiara D'Alpaos & Cesare Dosi & Michele Moretto, 2005. "Concession lenght and investment timing flexibility," Working Papers ubs0502, University of Brescia, Department of Economics.
    13. Cimpoiasu, Rodica, 2018. "New candidates for arbitrage-free stock price models via generalized conditional symmetry method," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 460-466.
    14. Panagiotidis, Theodore & Printzis, Panagiotis, 2020. "What is the investment loss due to uncertainty?," Global Finance Journal, Elsevier, vol. 45(C).
    15. Iglesias Vázquez, E.M. & Arranz Pérez, M., 2001. "Análisis de las relaciones entre el tipo de interés a corto plazo y su incertidumbre en Alemania, España y Suiza," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 19, pages 37-47, Diciembre.
    16. Carpenter, Jennifer N., 1998. "The exercise and valuation of executive stock options," Journal of Financial Economics, Elsevier, vol. 48(2), pages 127-158, May.
    17. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    18. Zhao, Hui & Rong, Ximin & Zhao, Yonggan, 2013. "Optimal excess-of-loss reinsurance and investment problem for an insurer with jump–diffusion risk process under the Heston model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 504-514.
    19. Gast¨®n S. Milanesi & Emilio El Alabi & Gabriela Pesce, 2015. "Continuity or Liquidation in Situations of Ambiguity: Fuzzy Binomial Model to Valuate Leveraged Firms," Research in Applied Economics, Macrothink Institute, vol. 7(1), pages 26-47, March.
    20. Robert J. Ritchey, 1990. "Call Option Valuation For Discrete Normal Mixtures," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 13(4), pages 285-296, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:196:y:2023:i:2:d:10.1007_s10957-022-02108-w. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.