AN APPROPRIATE APPROACH TO PRICING EUROPEAN-STYLE OPTIONS WITH THE ADOMIAN DECOMPOSITION METHOD

2018 ◽  
Vol 59 (3) ◽  
pp. 349-369
Author(s):  
ZIWIE KE ◽  
JOANNA GOARD ◽  
SONG-PING ZHU
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
European Options ◽  
Black Scholes Model ◽  
Adomian Decomposition ◽  
Black Scholes ◽  
Interest Rate Model ◽  
Vasicek Interest Rate Model ◽  
Digital Options ◽  
Continuous Estimation

We study the numerical Adomian decomposition method for the pricing of European options under the well-known Black–Scholes model. However, because of the nondifferentiability of the pay-off function for such options, applying the Adomian decomposition method to the Black–Scholes model is not straightforward. Previous works on this assume that the pay-off function is differentiable or is approximated by a continuous estimation. Upon showing that these approximations lead to incorrect results, we provide a proper approach, in which the singular point is relocated to infinity through a coordinate transformation. Further, we show that our technique can be extended to pricing digital options and European options under the Vasicek interest rate model, in both of which the pay-off functions are singular. Numerical results show that our approach overcomes the difficulty of directly dealing with the singularity within the Adomian decomposition method and gives very accurate results.

scholarly journals On Comparative Analysis for the Black-Scholes Model in the Generalized Fractional Derivatives Sense via Jafari Transform

2021 ◽  
Vol 2021 ◽  
pp. 1-22
Author(s):  
Saima Rashid ◽  
Sobia Sultana ◽  
Rehana Ashraf ◽  
Mohammed K. A. Kaabar
Keyword(s):  
Fractional Derivative ◽  
Adomian Decomposition Method ◽  
Capital Asset Pricing ◽  
Transform Method ◽  
Uniqueness Results ◽  
Black Scholes Model ◽  
Asset Pricing Models ◽  
Adomian Decomposition ◽  
Black Scholes ◽  
Generalized Fractional Derivatives

The Black-Scholes model is well known for determining the behavior of capital asset pricing models in the finance sector. The present article deals with the Black-Scholes model via the Caputo fractional derivative and Atangana-Baleanu fractional derivative operator in the Caputo sense, respectively. The Jafari transform is merged with the Adomian decomposition method and new iterative transform method. It is worth mentioning that the Jafari transform is the unification of several existing transforms. Besides that, the convergence and uniqueness results are carried out for the aforesaid model. In mathematical terms, the variety of equations and their solutions have been discovered and identified with various novel features of the projected model. To provide additional context for these ideas, numerous sorts of illustrations and tabulations are presented. The precision and efficacy of the proposed technique suggest its applicability for a variety of nonlinear evolutionary problems.

scholarly journals Solution of the Black-Scholes Equation: LDM and SDM

2021 ◽  
Vol 23 (07) ◽  
pp. 1111-1115
Author(s):  
R. K. Pavan Kumar. Pannala ◽  
Keyword(s):  
Differential Equation ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Decomposition Methods ◽  
Financial Mathematics ◽  
Discretization Method ◽  
Discretization Methods ◽  
Adomian Decomposition ◽  
Black Scholes ◽  
Laplace Decomposition Method

The main aim of this paper is to discuss a new way of a non-discretization method for the solution of the Black-Scholes equation. Black-Scholes is a mathematical model based on a partial differential equation. The solution of the model is of utmost importance in financial mathematics to estimate option pricing. Several analytical, numerical, and non-discretization methods are existing in the literature to solve the model. Two decomposition methods namely the Laplace decomposition method (LDM) and Sumudu decomposition method (SDM) are adopted for the present study. The results of the present techniques have closed an agreement with an approximate solution which has been obtained with the help of the Adomian Decomposition Method (ADM).

Nonlinear singular one dimensional thermo-elasticity coupled system and double Laplace decomposition methods

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6269-6280
Author(s):  
Hassan Gadain
Keyword(s):  
Laplace Transform ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Coupled System ◽  
Decomposition Methods ◽  
One Dimensional ◽  
Convergence Proof ◽  
Double Laplace Transform ◽  
Adomian Decomposition

In this work, combined double Laplace transform and Adomian decomposition method is presented to solve nonlinear singular one dimensional thermo-elasticity coupled system. Moreover, the convergence proof of the double Laplace transform decomposition method applied to our problem. By using one example, our proposed method is illustrated and the obtained results are confirmed.

scholarly journals Gaussons: optical solitons with log-law nonlinearity by Laplace–Adomian decomposition method

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 182-188
Author(s):  
O. González-Gaxiola ◽  
Anjan Biswas ◽  
Abdullah Kamis Alzahrani
Keyword(s):  
Numerical Simulations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Optical Solitons ◽  
Decomposition Scheme ◽  
Error Analyses ◽  
Adomian Decomposition ◽  
Log Law

AbstractThis paper presents optical Gaussons by the aid of the Laplace–Adomian decomposition scheme. The numerical simulations are presented both in the presence and in the absence of the detuning term. The error analyses of the scheme are also displayed.

scholarly journals A novel method for the analytical solution of fractional Zakharov–Kuznetsov equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Rasool Shah ◽  
Hassan Khan ◽  
Dumitru Baleanu ◽  
Poom Kumam ◽  
Muhammad Arif
Keyword(s):  
Present Method ◽  
Decomposition Method ◽  
Fractional Derivatives ◽  
Adomian Decomposition Method ◽  
Current Method ◽  
Analytical Technique ◽  
Suggested Technique ◽  
Adomian Decomposition ◽  
Novel Method ◽  
The Given

AbstractIn this article, an efficient analytical technique, called Laplace–Adomian decomposition method, is used to obtain the solution of fractional Zakharov– Kuznetsov equations. The fractional derivatives are described in terms of Caputo sense. The solution of the suggested technique is represented in a series form of Adomian components, which is convergent to the exact solution of the given problems. Furthermore, the results of the present method have shown close relations with the exact approaches of the investigated problems. Illustrative examples are discussed, showing the validity of the current method. The attractive and straightforward procedure of the present method suggests that this method can easily be extended for the solutions of other nonlinear fractional-order partial differential equations.

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