scholarly journals Fractional Black-Scholes model with regularized Prabhakar derivative

2017 ◽  
Vol 102 (116) ◽  
pp. 121-132 ◽  
Author(s):  
Shiva Eshaghi ◽  
Alireza Ansari ◽  
Reza Ghaziani ◽  
Mohammadreza Darani
Keyword(s):  
Analytical Solutions ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
European Options ◽  
Variational Iteration ◽  
Black Scholes Model ◽  
Approximate Analytical Solutions ◽  
Black Scholes ◽  
Fractional Type

We introduce a fractional type Black-Scholes model in European options including the regularized Prabhakar derivative. We apply the reconstruction of variational iteration method to get the approximate analytical solutions for some models of generalized fractional Black-Scholes equations in terms of the generalized Mittag-Leffler functions.

scholarly journals Coupling Technique of Haar Wavelet Transform and Variational Iteration Method for a Nonlinear Option Pricing Model

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1642
Author(s):  
Ruyi Xing ◽  
Meng Liu ◽  
Kexin Meng ◽  
Shuli Mei
Keyword(s):  
Iteration Method ◽  
Exact Analytical Solution ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Haar Wavelet ◽  
Algebraic Equations ◽  
Haar Wavelet Transform ◽  
Variational Iteration ◽  
Black Scholes Model ◽  
Black Scholes

Compared with the linear Black–Scholes model, nonlinear models are constructed through taking account of more practical factors, such as transaction cost, and so it is difficult to find an exact analytical solution. Combining the Haar wavelet integration method, which can transform the partial differential equation into the system of algebraic equations, the homotopy perturbation method, which can linearize the nonlinear problems, and the variational iteration method, which can solve the large system of algebraic equations efficiently, a novel numerical method for the nonlinear Black–Scholes model is proposed in this paper. Compared with the traditional methods, it has higher efficiency and calculation precision.

Examples of Analytical Solutions by Means of Mittag-Leffler Function of Fractional Black-Scholes Option Pricing Equation

2015 ◽  
Vol 18 (1) ◽  
Author(s):  
Mohammad Hossein Akrami ◽  
Gholam Hussian Erjaee
Keyword(s):  
Option Pricing ◽  
Analytical Solutions ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Financial Mathematics ◽  
Explicit Solutions ◽  
Analytical Technique ◽  
Variational Iteration ◽  
Black Scholes

AbstractIn this article, we have implemented reconstruction of variational iteration method as a new approximate analytical technique for solving fractional Black-Scholes option pricing equations. Indeed, we essentially use the well-known Mittag-Leffler function to obtain explicit solutions for some examples of financial mathematics equations.

scholarly journals APPLICATION OF ABOODH TRANSFORM ON SOME FRACTIONAL ORDER MATHEMATICAL MODELS

2020 ◽  
Vol 20 (3) ◽  
pp. 661-672
Author(s):  
JAWARIA TARIQ ◽  
JAMSHAD AHMAD
Keyword(s):  
Mathematical Models ◽  
Fractional Order ◽  
Analytical Solutions ◽  
Iteration Method ◽  
Analytical Techniques ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Physical Phenomena ◽  
Convergent Solution

In this work, a new emerging analytical techniques variational iteration method combine with Aboodh transform has been applied to find out the significant important analytical and convergent solution of some mathematical models of fractional order. These mathematical models are of great interest in engineering and physics. The derivative is in Caputo’s sense. These analytical solutions are continuous that can be used to understand the physical phenomena without taking interpolation concept. The obtained solutions indicate the validity and great potential of Aboodh transform with the variational iteration method and show that the proposed method is a good scheme. Graphically, the movements of some solutions are presented at different values of fractional order.

scholarly journals Variational Iteration Method for a Fractional-Order Brusselator System

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
H. Jafari ◽  
Abdelouahab Kadem ◽  
D. Baleanu
Keyword(s):  
Fractional Order ◽  
Fractional Differential Equations ◽  
Iteration Method ◽  
Fractional Derivatives ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Promising Tool ◽  
Approximate Analytical Solutions ◽  
Fractional Differential ◽  
Linear And Nonlinear

This paper presents approximate analytical solutions for the fractional-order Brusselator system using the variational iteration method. The fractional derivatives are described in the Caputo sense. This method is based on the incorporation of the correction functional for the equation. Two examples are solved as illustrations, using symbolic computation. The numerical results show that the introduced approach is a promising tool for solving system of linear and nonlinear fractional differential equations.

A NEWLY MODIFIED VARIATIONAL ITERATION METHOD FOR SOLVING NONLINEAR DIFFERENTIAL EQUATIONS

2013 ◽  
Vol 10 (05) ◽  
pp. 1350029
Author(s):  
R. YULITA MOLLIQ ◽  
M. S. M. NOORANI
Keyword(s):  
Iteration Method ◽  
Nonlinear Differential Equations ◽  
Method Comparison ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Accurate Method ◽  
Convergence Region ◽  
Variational Iteration ◽  
Approximate Analytical Solutions ◽  
Modified Variational Iteration Method

This paper presents a new reliable modification of the variational iteration method (MoVIM). An enlarged interval of convergence region of series solutions is obtained by inserting a nonzero auxiliary parameter (ℏ) into the correction functional of variational iteration method. Approximate analytical solutions for some examples of nonlinear problems are obtained using variational iteration method. Comparison with the exact solution, Runge–Kutta method 4, and also another modified variational iteration method has shown that MoVIM is an accurate method for solving nonlinear problems.

scholarly journals Adaptive Wavelet Precise Integration Method for Nonlinear Black-Scholes Model Based on Variational Iteration Method

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Huahong Yan
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Iteration Method ◽  
Integration Method ◽  
Variational Iteration Method ◽  
Precise Integration ◽  
Adaptive Wavelet ◽  
Precise Integration Method ◽  
Black Scholes Model ◽  
Black Scholes

An adaptive wavelet precise integration method (WPIM) based on the variational iteration method (VIM) for Black-Scholes model is proposed. Black-Scholes model is a very useful tool on pricing options. First, an adaptive wavelet interpolation operator is constructed which can transform the nonlinear partial differential equations into a matrix ordinary differential equations. Next, VIM is developed to solve the nonlinear matrix differential equation, which is a new asymptotic analytical method for the nonlinear differential equations. Third, an adaptive precise integration method (PIM) for the system of ordinary differential equations is constructed, with which the almost exact numerical solution can be obtained. At last, the famous Black-Scholes model is taken as an example to test this new method. The numerical result shows the method's higher numerical stability and precision.

scholarly journals Analytical solutions of time-fractional advection problem

2016 ◽  
Vol 12 (6) ◽  
pp. 6286-6289
Author(s):  
Huimin Wang
Keyword(s):  
Analytical Solutions ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
The Other ◽  
Variational Iteration

we use variational iteration method (VIM) to solve some nonlinear time-fractional advection problem.Compared to the other method, the VIM is direct and straightforward.

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