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<p>The aim of this study is to perform a theoretical analysis of the nonlinear fuzzy Black-Scholes-Barnblatt (BSB) equation using the methods of the Lie group to obtain exact solutions and determine its fundamental properties. The analysis of the Lie symmetries has yielded 11 symmetries that serve as building blocks for generating exact solutions to the equation. The direct method has helped to determine two conservation laws that reveal deep mathematical properties of the model framework. Two examples of European options are presented using the solutions obtained under the Lie symmetries for gold options priced from September 1, 2022 to August 1, 2023. The exact analytical solutions, together with a new understanding of option pricing under uncertainty, make the results of this study essential for the development of future fuzzy financial models.</p>

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Conservation laws and exact solutions for option pricing model with fuzzy parameters

  • 期刊论文

  • 发表日期：

    2026年6月30日

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  • Mohammad Hossein Seifi,
  • Elham Dastranj,
  • Hossein Sahebi Fard

摘要

The aim of this study is to perform a theoretical analysis of the nonlinear fuzzy Black-Scholes-Barnblatt (BSB) equation using the methods of the Lie group to obtain exact solutions and determine its fundamental properties. The analysis of the Lie symmetries has yielded 11 symmetries that serve as building blocks for generating exact solutions to the equation. The direct method has helped to determine two conservation laws that reveal deep mathematical properties of the model framework. Two examples of European options are presented using the solutions obtained under the Lie symmetries for gold options priced from September 1, 2022 to August 1, 2023. The exact analytical solutions, together with a new understanding of option pricing under uncertainty, make the results of this study essential for the development of future fuzzy financial models.