A new direct method for solving the Black–Scholes equation

Analytical Solutions of the Black–Scholes Pricing Model for European Option Valuation via a Projected Differential Transformation Method

“…Finally, we remarked that the PDTM is very efficient, reliable; and faster in application (even without giving up accuracy) when compared with the classical DTM [20], ADM [17], HAM and HPM [12]; though the results via these methods are in strong agreement. Hence, it is strongly recommended for both linear and nonlinear stochastic differential equations (SDEs) encountered in financial mathematics and other areas of applied sciences.…”

“…Algliardi, Popivanov and Slavova [16,17] Considering the solutions of linear and nonlinear Black-Scholes equations, other methods-Adomian Decomposition Method (ADM), modified ADM (MADM), modified VIM (MVIM), homotopy analysis method (HAM) and modified HAM (MHAM) are applied [23][24][25].…”

Efficient option valuation of single and double barrier options

“…Implementation of the aforementioned Mellin Maximum Entropy algorithm (MME) was done with the following major requirements in mind: a) to apply Mellin transform as described in [9] and [10]; b) to provide sufficient accuracy while maintaining very small error rates and keep the calculation time low; c) to provide a completely open code that relies solely on open packages which makes it possible to reuse the existing solution and reproduce our results;…”

“…Although there are many similar implementation available the one shown here is different in the following ways -it uses Mellin transform for option pricing as discussed in [9] and an algorithm developed in [10]; the main focus is put on providing sufficient accuracy while maintaining very small error rates and keeping the calculation time low; code is completely open and relies only on open packages which means that it can be used freely and without limitations or licensing issues.…”

Laplace Transform Homotopy Perturbation Method for the Two Dimensional Black Scholes Model with European Call Option

“…Since the option pricing in a market is dependent on other markets, the multidimensional Black Scholes equation is more efficient than the one dimensional version. There are various methods to find the solution of multidimensional Black Scholes model; for example, a radical basic function (RBF) method [2][3][4][5][6], the Mellin transform method [7], finite different method [8][9][10][11][12], a collection method with the quantic B-spline function [13], and homotopy perturbation method (HPM) [14,15].…”