An appropriate approach to pricing European-style options with the Adomian decomposition method

Digital Option Pricing Approach Using A Homotopy Perturbation Method

“…( 17) has a singularity and it is non-differentiable. In order to shift the singularity point to infinity, the transformation is given below [7]:…”

“…An exact solution of the Black Scholes equation has been obtained [1]. There are various methods to obtain an exact solution approach: Finite Difference Method [2], [3], Monte Carlo Method [4], Quintic B-spline collocation approach [5], Adomian Decomposition Method (ADM) [6], [7], Homotopy Perturbation Method (HPM) [8], [9], [10], etc.…”

“…which is a non-differentiable and non-smooth condition at S = K. Various approaches are used to solve non-differentiable and non-smooth problems, but a singularity point appears in the derivative. In [7], Ziwie This paper discusses the Black Scholes solution approach using HPM, where HPM is one of the approach solution methods in a power series, similar to the ADM. Digital options are the simplest type of options. The digital options have a payoff function as European options, which can not be derived at S = K. Using the variable transformation introduced in [7], we will apply it with HPM.…”

“…In [7], Ziwie This paper discusses the Black Scholes solution approach using HPM, where HPM is one of the approach solution methods in a power series, similar to the ADM. Digital options are the simplest type of options. The digital options have a payoff function as European options, which can not be derived at S = K. Using the variable transformation introduced in [7], we will apply it with HPM. The outline of this paper is organized as follows.…”

Constructing C0-Semigroups via Picard Iterations and Generating Functions: An Application to a Black–Scholes Integro-Differential Operator

“…When A is a differential operator in (1), successive approximations are also referred to as Picard iterations. Some authors [6][7][8][9] refer to the method of successive approximation as the Adomian decomposition method (ADM) [10] although for linear differential equations the ADM is basically a Picard iteration technique.…”