Approximate analytical solution for the Black-Scholes equation by method of lines

Abstract

The Stochastic Partial Differential Equations are part of a set of non-linear partial differential equations (PDE), which by their random behavior are difficult to solve analytically and numerically; One of them has been known as the Black-Scholes PDE since 1973, which determines the valuation of goods and/or assets called financial options. The development of the present work is to find numerical approximations to the solution of Black-Scholes PDE by the Method of Lines (MOL). The previous was achieved by means of a methodology based on an analytical study of the classic solution of the BlackScholes PDE. Finally, numerical methods and algorithms were applied to the Black Scholes PDE.

Solving fractional Black–Scholes equation by using Boubaker functions

“…It has shown its great capacity in this scope, and many scientists have been employed its results in their research and market analysis. There have some successful attempts to evaluate the approximate solution to the Black–Scholes model by researchers 13,14 . Furthermore, a wide variety of numerical approaches including explicit difference scheme, 15 Cauchy Euler method, 16 finite difference scheme, 17 and multivariate pad approximation scheme 18 have been used to evaluate the solution of Black–Scholes differential equations.…”