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Compound Option Pricing under Fuzzy Environment

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  • 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 , the -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, Hindawi, vol. 2014, pages 1-9, March.
    • Handle: RePEc:hin:jnljam:875319
    DOI: 10.1155/2014/875319
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    Cited by:

    1. Jorge de Andrés-Sánchez, 2023. "Fuzzy Random Option Pricing in Continuous Time: A Systematic Review and an Extension of Vasicek’s Equilibrium Model of the Term Structure," Mathematics, MDPI, vol. 11(11), pages 1-21, May.
    2. Xianfei Hui & Baiqing Sun & Hui Jiang & Indranil SenGupta, 2021. "Analysis of stock index with a generalized BN-S model: an approach based on machine learning and fuzzy parameters," Papers 2101.08984, arXiv.org, revised Feb 2022.
    3. Lin, Zhongguo & Han, Liyan & Li, Wei, 2021. "Option replication with transaction cost under Knightian uncertainty," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    4. 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.
    5. Silvia Muzzioli & Luca Gambarelli & Bernard Baets, 2020. "Option implied moments obtained through fuzzy regression," Fuzzy Optimization and Decision Making, Springer, vol. 19(2), pages 211-238, June.

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