Abstract
The Black-Scholes equation is one of the most significant mathematical models for a financial market. In this paper, the homotopy perturbation method is combined with Mohand transform to obtain the approximate solution of the fractional Black-Scholes European option pricing equation. The fractional derivative is considered in the Caputo sense. The process of the methods which produce solutions in terms of convergent series is explained. Some examples are given to show a powerful and efficient method to find approximate analytical solutions for fractional Black-Scholes European option pricing equation. Further, the same equation is solved by the homotopy perturbation Sumudu transform method. The results obtained by the two methods are in agreement.
Publisher
Omar Al-Mukhtar University
Reference22 articles.
1. Aggarwal, S., & Chauhan, R. (2019). A comparative study of Mohand and Aboodh transforms. International journal of research in advent Technology, 7(1), 520-529.
2. Aggarwal, S., Chauhan, R., & Sharma, N. (2018). Mohand transform of Bessel’s functions. International journal of research in advent Technology, 6(11), 3034-3038.
3. Aggarwal, S., Sharma, S. D., & Vyas, A. (2020). Mohand Transform for Handling Convolution Type Volterra Integro-Differential Equation of First Kind. International Journal of Latest Technology in Engineering, Management & Applied Science), IX(VII), 78-84.
4. Ankudinova, J., & Ehrhardt, M. (2008). On the numerical solution of nonlinear Black–Scholes equations. Computers & Mathematics with Applications, 56(3), 799-812.
5. Attaweel, M. E., & Almassry, H. (2020). On the Mohand Transform and Ordinary Differential Equations with Variable Coefficients. Al-Mukhtar Journal of Sciences, 35(1), 01-06.