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

• Published in: Mathematical modelling of natural phenomena Vol. 13; no. 1; p. 12
• Main Authors: Yavuz, M., Özdemir, N.
• Format: Journal Article
• Language: English
• Published: Les Ulis EDP Sciences 2018
• Subjects: 35R11; 49M27; 91G80; Adomian decomposition method; approximate-analytical solution; Black-Scholes equation; Conformable fractional derivative; Cybernetics; Differential equations; fractional option pricing equation; Iterative methods; Mathematical models; modified homotopy perturbation method; Operators (mathematics); Partial differential equations; Perturbation methods; Pricing; Stochastic models
• ISSN: 0973-5348; 1760-6101
• DOI: 10.1051/mmnp/2018009

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.