The finite volume method is known to be better for solving problems with hyperbolic partial differential equations (PDEs) or which can be written in conservative form including a source and/or diffusion term. These types of problems are mainly encountered in the modelling of transport phenomena in fluid mechanics. The main objective of the present work is to test classical finite volume method in another field, especially in financial area. For that we choose Black-Scholes’s linear model with constant parameters and the generalized linear model of Black-Scholes. Some authors for example in [10] have already solved those models but using other techniques of finite volume method. The first type of problems has an available analytical solution but not the second. The numerical solution of the first problem has been computed and compared with the analytical solution. The satisfactory results obtained in the constant parameters model allowed us to test the method in the generalized model.

Black-Scholes equation, European option, premium, strike price, maturity, classical finite volume method, numerical flux, diffusion term, source term.

Received: January 6, 2021; Accepted: January 18, 2021; Published: May 26, 2021

How to cite this article: Paré Daouda, Kassiénou Lamien, Longin Somé and Youssouf Paré, Solving Generalized Linear Model Of Black-Scholes With Classical Finite Volume Method, International Journal of Numerical Methods and Applications 20(1) (2021), 17-40. DOI: 10.17654/NM020010017

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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