This paper analyses the model of Black–Scholes option pricing from the point of view of the group theoretic approach. The study identified new independent variables that lead to the transformation of the Black–Scholes equation. Furthermore, corresponding determining equations were constructed and new symmetries were found. As a result, the findings of the study demonstrate of the integrability of the model to present an invariant solution for the Ornstein–Uhlenbeck stochastic process.

中文翻译：

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带有Ornstein-Uhlenbeck过程的Black-Scholes方程的不变解

本文从群体理论方法的角度分析了布莱克-斯科尔斯期权定价模型。该研究确定了导致Black-Scholes方程式转换的新自变量。此外，建立了相应的确定方程，并发现了新的对称性。结果，研究结果证明了该模型的可集成性，可以为Ornstein–Uhlenbeck随机过程提供不变的解。