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.

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.

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.

scholarly journals NUMERICAL SOLUTION FOR TIME-FRACTIONAL MURRAY REACTION-DIFFUSION EQUATIONS VIA REDUCED DIFFERENTIAL TRANSFORM METHOD

2021 ◽  
Author(s):  
Muhammed Yiğider ◽  
Serkan Okur
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Differential Transform Method ◽  
Reaction Diffusion Equations ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Differential ◽  
Reduced Differential Transform Method ◽  
Time Fractional Differential Equations

In this study, solutions of time-fractional differential equations that emerge from science and engineering have been investigated by employing reduced differential transform method. Initially, the definition of the derivatives with fractional order and their important features are given. Afterwards, by employing the Caputo derivative, reduced differential transform method has been introduced. Finally, the numerical solutions of the fractional order Murray equation have been obtained by utilizing reduced differential transform method and results have been compared through graphs and tables. Keywords: Time-fractional differential equations, Reduced differential transform methods, Murray equations, Caputo fractional derivative.

Solution of Free Vibration Equations of Euler-Bernoulli Cracked Beams by Using Differential Transform Method

2011 ◽  
Vol 110-116 ◽  
pp. 4532-4536 ◽  
Author(s):  
K. Torabi ◽  
J. Nafar Dastgerdi ◽  
S. Marzban
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Differential Transform Method ◽  
Beam Model ◽  
Cracked Beam ◽  
Transform Method ◽  
Simple Method ◽  
Differential Transform

In this paper, free vibration differential equations of cracked beam are solved by using differential transform method (DTM) that is one of the numerical methods for ordinary and partial differential equations. The Euler–Bernoulli beam model is proposed to study the frequency factors for bending vibration of cracked beam with ant symmetric boundary conditions (as one end is clamped and the other is simply supported). The beam is modeled as two segments connected by a rotational spring located at the cracked section. This model promotes discontinuities in both vertical displacement and rotational due to bending. The differential equations for the free bending vibrations are established and then solved individually for each segment with the corresponding boundary conditions and the appropriated compatibility conditions at the cracked section by using DTM and analytical solution. The results show that DTM provides simple method for solving equations and the results obtained by DTM converge to the analytical solution with much more accurate for both shallow and deep cracks. This study demonstrates that the differential transform is a feasible tool for obtaining the analytical form solution of free vibration differential equation of cracked beam with simple expression.

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