Purpose
The purpose of this paper is to evaluate a European option using the fractional version of the Black-Scholes model.
Design/methodology/approach
In this paper, the authors employ the block-pulse operational matrix algorithm to approximate the solution of the fractional Black-Scholes equation with the initial condition for a European option pricing problem.
Findings
The fractional derivative will be described in the Caputo sense in this paper. The authors show the accuracy and computational efficiency of the proposed algorithm through some numerical examples.
Originality/value
This is the first paper that considers an alternative algorithm for pricing a European option using the fractional Black-Scholes model.
Laplace transform and new homotopy perturbation methods are adopted to study Fisher-type equations analytically. The solutions introduced in this study can be used to obtain the closed form of the solutions if they are required. The combined method needs less work in comparison with the other homotopy perturbation methods and decreases volume of calculations considerably. The method is tested on various examples, and results show that new method is more effective and convenient to use, and high accuracy of it is evident.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.