BSM model for ML-payoff function through PDTM

2018 ◽  
Vol 13 (01) ◽  
pp. 2050024
Author(s):  
S. J. Ghevariya
Keyword(s):  
Information Theory ◽  
Option Pricing ◽  
Payoff Function ◽  
Differential Transform Method ◽  
Entropy Function ◽  
European Option ◽  
Transform Method ◽  
European Option Pricing ◽  
Black Scholes ◽  
Differential Transform

This paper contributes to the valuation of Black–Scholes–Merton (BSM) European option pricing formula for Modified Log-payoff (ML-payoff) function, [Formula: see text] through Projected Differential Transform Method (PDTM). The ML-payoff function is closely related with the entropy function [Formula: see text] in Information Theory. It turns out that the present BSM formula is quite close to the celebrated plain vanilla option.

Solution of time fractional Black-Scholes European option pricing equation arising in financial market

2016 ◽  
Vol 5 (4) ◽  
Author(s):  
A.S.V. Ravi Kanth ◽  
K. Aruna
Keyword(s):  
Boundary Conditions ◽  
Option Pricing ◽  
Financial Market ◽  
Differential Transform Method ◽  
European Option ◽  
Transform Method ◽  
European Option Pricing ◽  
Black Scholes ◽  
Differential Transform ◽  
Fractional Differential

AbstractIn this paper, we present fractional differential transform method (FDTM) and modified fractional differential transform method (MFDTM) for the solution of time fractional Black-Scholes European option pricing equation. The method finds the solution without any discretization, transformation, or restrictive assumptions with the use of appropriate initial or boundary conditions. The efficiency and exactitude of the proposed methods are tested by means of three examples.

A fractional reduced differential transform method for solving time fractional Black Scholes American option pricing equation

2021 ◽  
Vol 30 (1) ◽  
pp. 1-10
Author(s):  
MANZOOR AHMAD ◽  
RAJSHREE MISHRA ◽  
RENU JAIN
Keyword(s):  
Option Pricing ◽  
American Option ◽  
Differential Transform Method ◽  
American Option Pricing ◽  
Transform Method ◽  
Put Options ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Differential Transform ◽  
Reduced Differential Transform Method

In this paper, fractional reduced differential transform method (FRDTM) is operated to solve time fractional Black-Scholes American option pricing equation paying no dividends.The Black-Scholes model plays a significant role in the evaluation of European or American call and put options. The advantage of the proposed method to other existing methods is that it finds the solution without discretization or transformation. While using this method, no recommended assumptions are needed and hence the computational work reduces to a greater extent. Numerical experiments prove that the proposed method is efficient and valid for obtaining the solution of time fractional Black-Scholes equation governing American options. This method proves to be powerful for solving general fractional order partial differential equations (PDEs) existing in the field of Science, Engineering and other related fields.

On the Black-Scholes European Option Pricing Model Robustness and Generality

2008 ◽  
Author(s):  
Hellinton Hatsuo Takada ◽  
José de Oliveira Siqueira ◽  
Marcelo de Souza Lauretto ◽  
Carlos Alberto de Bragança Pereira ◽  
Julio Michael Stern
Keyword(s):  
Option Pricing ◽  
Pricing Model ◽  
European Option ◽  
European Option Pricing ◽  
Black Scholes ◽  
Option Pricing Model ◽  
Model Robustness

scholarly journals Laplace Decomposition Method for Solving Fractional Black-Scholes European Option Pricing Equation

2020 ◽  
Vol 1 (4) ◽  
pp. 194-207
Author(s):  
Abiodun Ezekiel Owoyemi ◽  
Ira Sumiati ◽  
Endang Rusyaman ◽  
Sukono Sukono
Keyword(s):  
Differential Equations ◽  
Fractional Calculus ◽  
Option Pricing ◽  
Decomposition Method ◽  
European Option ◽  
Partial Differential ◽  
European Option Pricing ◽  
Black Scholes ◽  
Pricing Problems ◽  
Laplace Decomposition Method

Fractional calculus is related to derivatives and integrals with the order is not an integer. Fractional Black-Scholes partial differential equation to determine the price of European-type call options is an application of fractional calculus in the economic and financial fields. Laplace decomposition method is one of the reliable and effective numerical methods for solving fractional differential equations. Thus, this paper aims to apply the Laplace decomposition method for solving the fractional Black-Scholes equation, where the fractional derivative used is the Caputo sense. Two numerical illustrations are presented in this paper. The results show that the Laplace decomposition method is an efficient, easy and very useful method for finding solutions of fractional Black-Scholes partial differential equations and boundary conditions for European option pricing problems.

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