Modulation instability and solitary wave analysis of the Ivancevic option pricing model via Novel mathematical techniques

Mehdi, Khush Bukht; Baloch, Sajawal Abbas; Siddique, Imran; Abduvalieva, Dilsora; Yaseen, Zaher M; Ahmad, Hijaz

doi:10.22034/cmde.2025.67141.3185

Modulation instability and solitary wave analysis of the Ivancevic option pricing model via Novel mathematical techniques

Document Type : Research Paper

Authors

¹ Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan.

² Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan.

³ 1. Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan. 2. Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan. 3. Mathematics in Applied Sciences and Engineering Research Group, Scientific Research Center, Al-Ayen University, Nasiriyah, 64001, Iraq.

⁴ Department of Mathematics and Information Technologies, Tashkent State Pedagogical University, Bunyodkor avenue, 27, Tashkent, 100070, Uzbekistan.

⁵ Civil and Environmental Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.

⁶ 1. Operational Research Center in Healthcare, Near East University, Nicosia/TRNC, 99138 Mersin 10, Turkey. 2. Department of Mathematics, College of Science, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, South Korea. 3. Engineered Biomaterials Research Center, Khazar University, Baku, Azerbaijan.

10.22034/cmde.2025.67141.3185

Abstract

In academia, financial engineering challenges are very important, and there is an ongoing demand for effective ways to examine and evaluate these models. The new extended direct algebraic approach and the new auxiliary equation method have been used in this study to investigate the analytical solutions of the economically significant model known as the Ivancevic option pricing model (IOPM) in the sense of a new definition of M-truncated derivative. Additionally, we will examine the equation’s modulation instability (MI) using linear stability approach that demonstrates the accuracy and stability of all combined solutions. The analytical method of this model is infrequently observed in the literature, despite the fact that numerous scholars have examined its applicability and feasibility. The regulated Brownian motion associated with a non-linear Schr¨odinger type equation is described by this model. Mathematical approaches are applied to generate the solution to understand the fluctuations in market prices for the proposed model. The reaction of system to pulse propagation is explained through the use of graphical representations in 2D, contour and 3D forms. Anticipating suitable parameter values that correspond with the observed data is made possible by these illustrations. The sensitivity analysis predicts the model’s dependence on the initial conditions. The findings of this study indicated that the suggested approaches preserved the physical characteristics present in realistic processes while providing a very dependable and adaptable substitute for problem-solving. Furthermore, we guarantee that all of the results demonstrate that these techniques are a useful mathematical tool for identifying precise solitary wave solutions to nonlinear models that are present in various scientific and technical domains.

Keywords

Main Subjects

Computational methods for problems pertaining to economics, and finance

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