Kaixi Zhang

With the development of uncertain finance, uncertain stock models have become increasingly popular for modeling stock prices. This paper explores the symmetric properties inherent in the uncertain mean-reverting stock model, particularly in the structure of its differential equations and the resulting pricing formulas. The primary findings comprise the derivation of explicit pricing formulas, via uncertain differential equations, for European, American, Asian, and geometric average Asian options under the uncertain mean-reverting stock model. The symmetry in the inverse uncertainty distributions and the duality between call and put options are highlighted, demonstrating the model’s alignment with symmetric financial principles. Furthermore, several numerical examples are provided to illustrate the applicability and the symmetry-related characteristics of the derived formulas.