Analytical Solutions of Black-Scholes Partial Differential Equation of Pricing for Valuations of Financial Options using Hybrid Transformation Methods

Authors

  • Zainab Olabisi Dere Department of Mathematics, Florida State University, USA
  • Gbeminiyi Musibau Sobamowo Department of Mechanical Engineering, Faculty of Engineering, University of Lagos, Akoka Lagos, Nigeria
  • Antonio Marcos de Oliveira Siqueira Federal University of Viçosa, Brazil https://orcid.org/0000-0001-9334-0394

DOI:

https://doi.org/10.18540/jcecvl8iss1pp15223-01i

Keywords:

Black–Scholes model; Partial differential Equation; Financial Market; Option pricing; Laplace-differential transformation method.

Abstract

Black–Scholes partial differential equation is a generally acceptable model in financial markets for option pricing. However, without variable transformations, the provision of symbolic solutions to the variable coefficient partial differential equation is not a straight-forward task. Moreover, the coefficients of the Black–Scholes can depend on the time and the asset price which makes the analytical solution of the Black–Scholes model very difficult to develop. In this paper, analytical solutions of the model of valuations of financial options are presented using Laplace and differential transform methods. The results of the solutions of the Laplace and differential transformation methods are compared with the results of the exact analytical solutions. Moreover, numerical examples for different options pricing are presented to establish the applications, speed and accuracy of the hybrid methods.

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Published

2022-06-01

How to Cite

Dere, Z. O., Sobamowo, G. M., & Siqueira, A. M. de O. (2022). Analytical Solutions of Black-Scholes Partial Differential Equation of Pricing for Valuations of Financial Options using Hybrid Transformation Methods. The Journal of Engineering and Exact Sciences, 8(1), 15223–01i. https://doi.org/10.18540/jcecvl8iss1pp15223-01i

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