Soliton theory and modulation instability analysis: The Ivancevic option pricing model in economy

In this projected paper, we study on the Ivancevic option pricing model. We apply two important methods, namely, rational sine-Gordon expansion method which is recently developed, and secondly, modified exponential method. Via these methods, we obtain some important properties of Ivancevic option pricing model. We extract many solutions such as complex, periodic, dark bright, mixed dark-bright, singular, travelling and hyperbolic functions. We investigate the option price wave functions of dependent variable, and also, observe the modulation instability analysis in detail. Furthermore, we report the strain conditions for the valid solutions under the family conditions, as well. We simulate the 2D, 3D and counter plots by choosing the suitable values of the parameters involved. Finally, we present the top and low points of pricing in the mentioned intervals via contour simulations. (C) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.