Application of propagating solitons to Ivancevic option pricing governing model and construction of first integral by Nucci's direct reduction approach

The current research aims to analyze the Ivancevic option pricing model and investigate its soliton solutions, which offer a comprehensive understanding of various related phenomena. The equation's Cauchy problem cannot be resolved through the inverse scattering transform, necessitating an analytical approach for accurate traveling wave solutions. To achieve this, the study employs the generalized logistic equation method and Nucci's reduction approaches to derive solitary wave solutions. Moreover, Nucci's reduction procedure is applied to formulate the first integral of a differential equation, ensuring conservation and exact solutions. In order to gauge the Ivancevic option pricing equation's sensitivity, a sensitivity analysis is conducted. At the end, the chaotic behavior of the considered model with the perturbed term is examined by using Lyapunov exponent approach.