Solving the general form of the fractional Black–Scholes with two assets through Reconstruction Variational Iteration Method

Abstract

The objective of this study is to examine the dynamic components of option pricing in the European put option market by utilizing the two-dimensional time fractional-order Black–Scholes equation. To enhance the classical Black–Scholes equation, we utilize the Caputo type of the Katugampola fractional derivative. The Reconstruction of Variational Iteration Method is employed as a powerful tool for analyzing option price behavior in the European-style market. In our investigation, we utilize this method to obtain an exact solution for fractional Black–Scholes with two assets. Moreover, the findings demonstrate the impressive effectiveness of the Reconstruction of Variational Iteration Method in addressing two-dimensional fractional-order differential equations, thereby highlighting its potential as a valuable numerical solution technique.