Analytical Solutions of Black-Scholes Partial Differential Equation of Pricing for Valuations of Financial Options using Hybrid Transformation Methods
DOI:
https://doi.org/10.18540/jcecvl8iss1pp15223-01iPalavras-chave:
Black–Scholes model; Partial differential Equation; Financial Market; Option pricing; Laplace-differential transformation method.Resumo
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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Copyright (c) 2022 The Journal of Engineering and Exact Sciences
Este trabalho está licenciado sob uma licença Creative Commons Attribution 4.0 International License.