Results 11 to 20 of about 3,326,698 (171)

Novel Approaches for Getting the Solution of the Fractional Black–Scholes Equation Described by Mittag-Leffler Fractional Derivative

Discrete Dynamics in Nature and Society, 2020
The value of an option plays an important role in finance. In this paper, we use the Black–Scholes equation, which is described by the nonsingular fractional-order derivative, to determine the value of an option. We propose both a numerical scheme and an
Ndolane Sene, Babacar Sène, Seydou Nourou Ndiaye, Awa Traoré   +3 more
doaj   +2 more sources

Nonuniform Finite Difference Scheme for the Three-Dimensional Time-Fractional Black–Scholes Equation

Journal of Function Spaces, 2021
In this study, we present an accurate and efficient nonuniform finite difference method for the three-dimensional (3D) time-fractional Black–Scholes (BS) equation.
Sangkwon Kim, Chaeyoung Lee, Wonjin Lee, Soobin Kwak, Darae Jeong, Junseok Kim   +5 more
doaj   +2 more sources

Solution of the Fractional Black-Scholes Option Pricing Model by Finite Difference Method [PDF]

Abstract and Applied Analysis, 2013
This work deals with the put option pricing problems based on the time-fractional Black-Scholes equation, where the fractional derivative is a so-called modified Riemann-Liouville fractional derivative.
Lina Song, Weiguo Wang
doaj   +2 more sources

Using a Mix of Finite Difference Methods and Fractional Differential Transformations to Solve Modified Black–Scholes Fractional Equations

Mathematics
This paper discusses finding solutions to the modified Fractional Black–Scholes equation. As is well known, the options theory is beneficial in the stock market.
Agus Sugandha, Endang Rusyaman, Sukono, Ema Carnia   +3 more
doaj   +2 more sources

A hybrid Chelyshkov wavelet-finite differences method for time-fractional black-Scholes equation [PDF]

Journal of Mahani Mathematical Research
In this paper, a hybrid method for solving time-fractional Black-Scholes equation is introduced for option pricing. The presented method is based on time and space discretization.
Seyyed Amjad Samareh Hashemi, Habibollah Saeedi, Ali Foroush Bastani   +2 more
doaj   +3 more sources

The modified homotopy perturbation method and its application to the dynamics of price evolution in Caputo-fractional order Black Scholes model

Beni-Suef University Journal of Basic and Applied Sciences, 2023
Background Following a financial loss in trades due to lack of risk management in previous models from market practitioners, Fisher Black and Myron Scholes visited the academic setting and were able to mathematically develop an option pricing equation ...
Adedapo Ismaila Alaje, Morufu Oyedunsi Olayiwola, Kamilu Adewale Adedokun, Joseph Adeleke Adedeji, Asimiyu Olamilekan Oladapo, Yunus Olanrewaju Akeem   +5 more
doaj   +1 more source

On the solution of two-dimensional fractional Black–Scholes equation for European put option

Advances in Difference Equations, 2020
The purpose of this paper was to investigate the dynamics of the option pricing in the market through the two-dimensional time fractional-order Black–Scholes equation for a European put option.
Din Prathumwan, Kamonchat Trachoo
doaj   +1 more source

Approximation of Caputo Fractional Derivative and Numerical Solutions of Fractional Differential Equations

Fractal and Fractional, 2023
In this paper, we consider an approximation of the Caputo fractional derivative and its asymptotic expansion formula, whose generating function is the polylogarithm function.
Yuri Dimitrov, Slavi Georgiev, Venelin Todorov   +2 more
doaj   +1 more source

Robust option replication for a Black-Scholes model extended with nondeterministic trends [PDF]

, 2012
Statistical analysis on various stocks reveals long range dependence behavior of the stock prices that is not consistent with the classical Black and Scholes model.
Schoenmakers, John G. M., Kloeden, Peter E.   +1 more
core   +1 more source

On a Multigrid Method for Tempered Fractional Diffusion Equations

Fractal and Fractional, 2021
In this paper, we develop a suitable multigrid iterative solution method for the numerical solution of second- and third-order discrete schemes for the tempered fractional diffusion equation.
Linlin Bu, Cornelis W. Oosterlee
doaj   +1 more source