IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2014y2014i1n875319.html

Compound Option Pricing under Fuzzy Environment

Author

Listed:
  • Xiandong Wang
  • Jianmin He
  • Shouwei Li

Abstract

Considering the uncertainty of a financial market includes two aspects: risk and vagueness; in this paper, fuzzy sets theory is applied to model the imprecise input parameters (interest rate and volatility). We present the fuzzy price of compound option by fuzzing the interest and volatility in Geske’s compound option pricing formula. For each α, the α‐level set of fuzzy prices is obtained according to the fuzzy arithmetics and the definition of fuzzy‐valued function. We apply a defuzzification method based on crisp possibilistic mean values of the fuzzy interest rate and fuzzy volatility to obtain the crisp possibilistic mean value of compound option price. Finally, we present a numerical analysis to illustrate the compound option pricing under fuzzy environment.

Suggested Citation

  • Xiandong Wang & Jianmin He & Shouwei Li, 2014. "Compound Option Pricing under Fuzzy Environment," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:875319
    DOI: 10.1155/2014/875319
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2014/875319
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/875319?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
    ---><---

    References listed on IDEAS

    as
    1. Zhang, Li-Hua & Zhang, Wei-Guo & Xu, Wei-Jun & Xiao, Wei-Lin, 2012. "The double exponential jump diffusion model for pricing European options under fuzzy environments," Economic Modelling, Elsevier, vol. 29(3), pages 780-786.
    2. repec:bla:jfinan:v:43:y:1988:i:5:p:1235-56 is not listed on IDEAS
    3. Geske, Robert, 1979. "The valuation of compound options," Journal of Financial Economics, Elsevier, vol. 7(1), pages 63-81, March.
    4. Lee, Meng-Yu & Yeh, Fang-Bo & Chen, An-Pin, 2008. "The generalized sequential compound options pricing and sensitivity analysis," Mathematical Social Sciences, Elsevier, vol. 55(1), pages 38-54, January.
    5. Elettra, Agliardi & Rossella, Agliardi, 2003. "A generalization of the Geske formula for compound options," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 75-82, February.
    6. Geske, Robert & Johnson, Herb E, 1984. "The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-1524, December.
    7. Susanne Griebsch, 2013. "The evaluation of European compound option prices under stochastic volatility using Fourier transform techniques," Review of Derivatives Research, Springer, vol. 16(2), pages 135-165, July.
    8. Yu-Lin Huang & Chai-Chi Pi, 2009. "Valuation of multi-stage BOT projects involving dedicated asset investments: a sequential compound option approach," Construction Management and Economics, Taylor & Francis Journals, vol. 27(7), pages 653-666.
    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. Zhang, Weiting & He, Guitian & Luo, Maokang & Liang, Wenjie, 2025. "Valuation of R&D projects of new energy vehicles based on generalized mixed sub-fractional Brownian motion under fuzzy environment," Applied Mathematics and Computation, Elsevier, vol. 507(C).
    2. Andrejs Čirjevskis, 2022. "A Discourse on Foresight and the Valuation of Explicit and Tacit Synergies in Strategic Collaborations," JRFM, MDPI, vol. 15(7), pages 1-18, July.

    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. Wang, Xiandong & He, Jianmin, 2017. "A simple method for generalized sequential compound options pricing," Mathematical Social Sciences, Elsevier, vol. 87(C), pages 85-91.
    2. Yu-Lin Huang & Tsen-Chin Lin, 2023. "Compound deferrable options for the valuation of multi-stage infrastructure investment projects," Construction Management and Economics, Taylor & Francis Journals, vol. 41(8), pages 670-686, August.
    3. Lee, Meng-Yu & Yeh, Fang-Bo & Chen, An-Pin, 2008. "The generalized sequential compound options pricing and sensitivity analysis," Mathematical Social Sciences, Elsevier, vol. 55(1), pages 38-54, January.
    4. Agliardi, Rossella, 2006. "Options to expand: Some remarks," Finance Research Letters, Elsevier, vol. 3(1), pages 65-72, March.
    5. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    6. Chung, Y. Peter & Johnson, Herb, 2011. "Extendible options: The general case," Finance Research Letters, Elsevier, vol. 8(1), pages 15-20, March.
    7. 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.
    8. Susanne Griebsch, 2013. "The evaluation of European compound option prices under stochastic volatility using Fourier transform techniques," Review of Derivatives Research, Springer, vol. 16(2), pages 135-165, July.
    9. Cosma, Antonio & Galluccio, Stefano & Scaillet, Olivier, 2012. "Valuing American options using fast recursive projections," Working Papers unige:41856, University of Geneva, Geneva School of Economics and Management.
    10. Engelen, Peter-Jan & Kool, Clemens & Li, Ye, 2016. "A barrier options approach to modeling project failure: The case of hydrogen fuel infrastructure," Resource and Energy Economics, Elsevier, vol. 43(C), pages 33-56.
    11. Faninam, Farzan, 2024. "Essays on real options : Triopoly dynamics, disconnected investment regions, and multiple investment options," Other publications TiSEM cccc1cad-2899-4b57-9d83-f, Tilburg University, School of Economics and Management.
    12. Ming-Cheng WU & I-Cheng LIN & Yi-Ting HUANG & Chang-Rong, 2015. "Forecasting Prices Of Presale Houses: A Real Option Approach," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(1), pages 143-158, March.
    13. Minqiang Li, 2010. "A quasi-analytical interpolation method for pricing American options under general multi-dimensional diffusion processes," Review of Derivatives Research, Springer, vol. 13(2), pages 177-217, July.
    14. Mondher Bellalah, 2009. "Derivatives, Risk Management & Value," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7175, September.
    15. Forte, Santiago, 2004. "Capital structure: optimal leverage and maturity choice in a dynamic model," DEE - Working Papers. Business Economics. WB wb041206, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    16. Cosma, Antonio & Galluccio, Stefano & Pederzoli, Paola & Scaillet, Olivier, 2020. "Early Exercise Decision in American Options with Dividends, Stochastic Volatility, and Jumps," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(1), pages 331-356, February.
    17. Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Derivative Security Pricing," Dynamic Modeling and Econometrics in Economics and Finance, Springer, edition 127, number 978-3-662-45906-5, June.
    18. L. Sereno, 2006. "Valuing R & D Investments With A Jump-Diffusion Process," Working Papers 569, Dipartimento Scienze Economiche, Universita' di Bologna.
    19. Jonathan Ziveyi, 2011. "The Evaluation of Early Exercise Exotic Options," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2011, January-A.
    20. Foad Shokrollahi, 2017. "Pricing compound and extendible options under mixed fractional Brownian motion with jumps," Papers 1708.04829, arXiv.org.

    More about this item

    Statistics

    Access and download statistics

    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:wly:jnljam:v:2014:y:2014:i:1:n:875319. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4185 .

    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.