Approximate Solution of Time-Fractional Ivancevic Option Pricing Model

Abstract

Option pricing is a vital area in financial mathematics that consists of the development of efficient models. The Ivancevic Option Pricing Model (IOPM) is a wave-based, nonlinear, adaptive version of the traditional Black-Scholes (BS) model. In this work, we use an efficient method to find approximate solutions to the time-fractional IOPM. The fractional derivative is treated using two types of kernels, namely singular and nonsingular. Convergence and the uniqueness of the proposed method are also discussed. Two test problems of adaptive market potential that are nonzero are examined to illustrate the method efficiency, simplicity, and straightforwardness in its application. Results are presented in 2D and 3D graphs to understand the behaviour of the solutions.