The Fractional Soliton Wave Propagation of Non-Linear Volatility and Option Pricing Systems with a Sensitive Demonstration

In this study, we explore a fractional non-linear coupled option pricing and volatility system. The model under consideration can be viewed as a fractional non-linear coupled wave alternative to the Black–Scholes option pricing governing system, introducing a leveraging effect where stock volatility corresponds to stock returns. Employing the inverse scattering transformation, we find that the Cauchy problem for this model is insolvable. Consequently, we utilize the Φ6-expansion algorithm to generate generalized novel solitonic analytical wave structures within the system. We present graphical representations in contour, 3D, and 2D formats to illustrate how the system’s behavior responds to the propagation of pulses, enabling us to predict suitable parameter values that align with the data. Finally, a conclusion is given.