Optimizing option pricing: Exact and approximate solutions for the time-fractional Ivancevic model

Abstract

This research investigates the time fractional Ivancevic option pricing model and presents two distinct solution methods: the invariant subspace method for obtaining exact solutions and the residual power series method for generating approximate solutions. In the invariant subspace method, we employ an algebraic approach to solve the time fractional Ivancevic option pricing model. By constructing an appropriate invariant subspace, we derive a system of fractional ordinary differential equations that characterizes the exact solution. This method provides a rigorous and efficient technique for generating various exact solutions. We also propose the residual power series method for obtaining approximate solutions. This method involves expressing the solution as an expansion of power functions and iteratively solving the residual equation to refine the approximation. By truncating the series expansion, we obtain an approximate solution that captures the essential features of the model while balancing computational efficiency and accuracy. Different graphs in 2-dimensions and 3-dimensions are presented to pioneer the obtained solutions. Our findings demonstrate the effectiveness of the invariant subspace method in generating exact solutions and shedding light on the model's dynamics. The residual power series method, on the other hand, provides a flexible and computationally efficient approach for obtaining reliable approximate solutions. The integration of exact and approximate methodologies presents a thorough structure for evaluating and valuing options in the time fractional Ivancevic option pricing model. This comprehensive approach yields valuable understandings for financial professionals and researchers alike.