A different approach to the European option pricing model with new fractional operator

¹ Faculty of Science, Department of Mathematics-Computer Sciences, Necmettin Erbakan University, 42090 Konya, Turkey
² Faculty of Sciences and Arts, Department of Mathematics, Balikesir University, 10145 Balikesir, Turkey

^* Corresponding author: mehmetyavuz@konya.edu.tr

Received: 3 October 2017
Accepted: 23 October 2017

Abstract

In this work, we have derived an approximate solution of the fractional Black-Scholes models using an iterative method. The fractional differentiation operator used in this paper is the well-known conformable derivative. Firstly, we redefine the fractional Black-Scholes equation, conformable fractional Adomian decomposition method (CFADM) and conformable fractional modified homotopy perturbation method (CFMHPM). Then, we have solved the fractional Black-Scholes (FBS) and generalized fractional Black-Scholes (GFBS) equations by using the proposed methods, which can analytically solve the fractional partial differential equations (FPDE). In order to show the efficiencies of these methods, we have compared the numerical and exact solutions of these two option pricing problems by using in pricing the actual market data. Also, we have found out that the proposed models are very efficient and powerful techniques in finding approximate solutions of the fractional Black-Scholes models which are considered in conformable sense.