Wave Solutions and Dynamical Behavior of the Ivancevic Option Pricing Model

This paper investigates exact analytical solutions of the Ivancevic option pricing model, a nonlinear mathematical framework designed to describe complex features of financial markets, including market volatility and nonlinear asset price dynamics. Unlike classical option pricing models, the Ivancevic model incorporates nonlinear wave behavior, making it suitable for capturing irregular and extreme market movements. To obtain closed-form solutions, the modified extended direct algebraic method is employed as an effective analytical tool. Through this approach, several families of exact wave solutions are derived, including periodic, dark-bright, mixed dark–bright, singular, and hyperbolic function solutions. These solution structures reveal a wide range of possible option price behaviors under different market conditions and parameter settings. To further understand the economic and dynamical implications of the obtained solutions, numerical simulations are carried out using carefully selected model parameters. The numerical analysis includes two- and three-dimensional wave profiles as well as contour plots, which provide clear visual insight into the evolution and interaction of pricing waves over time and space. In particular, contour plots are used to identify the extrema and concentration regions of option price fluctuations within specified temporal and spatial intervals. These visualizations help clarify the influence of model parameters on market dynamics. Overall, the results enhance the analytical understanding of the Ivancevic option pricing model and demonstrate the effectiveness of the proposed method. The findings offer a solid mathematical foundation for future research on stability analysis, parameter sensitivity, and nonlinear wave propagation in complex financial and economic systems.