Results 81 to 90 of about 228 (169)

Solving Black-Schole Equation Using Standard Fractional Brownian Motion

Journal of Mathematics Research, 2019
In this paper, we emphasize the Black-Scholes equation using standard fractional Brownian motion BHwith the hurst index H ∈ [0,1]. N. Ciprian (Necula, C. (2002)) and Bright and Angela (Bright, O., Angela, I., & Chukwunezu (2014)) get the same formula for the evaluation of a Call and Put of a fractional European with the different ...
Didier Alain Njamen Njomen, Eric Djeutcha   +1 more
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Fractional Order Stochastic Differential Equation with Application in European Option Pricing

Discrete Dynamics in Nature and Society, 2014
Memory effect is an important phenomenon in financial systems, and a number of research works have been carried out to study the long memory in the financial markets.
Qing Li, Yanli Zhou, Xinquan Zhao, Xiangyu Ge   +3 more
doaj   +1 more source

A Robust Numerical Simulation of a Fractional Black–Scholes Equation for Pricing American Options

Journal of Nonlinear Mathematical Physics
Abstract After the discovery of fractal structures of financial markets, fractional partial differential equations (fPDEs) became very popular in studying dynamics of financial markets. Available research results involves two key modelling aspects; firstly, derivation of tractable asset pricing models, those that closely reflects the actual ...
Patidar, Kailash C, Nuugulu, S M, Gideon, F   +2 more
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Numerical methods for fractional Black-Scholes equations and their applications to option pricing

, 2023
This thesis focuses on the modification of the classical Black-Scholes equation by introducing fractional derivatives instead of the usual integer order derivatives. The project has two main parts: (1) develop efficient numerical methods, such as finite difference methods and a space-time spectral method, for the resulting fractional partial ...
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Approximate Solution for Fractional Black-Scholes European Option Pricing Equation

Al-Mukhtar Journal of Sciences, 2023
The Black-Scholes equation is one of the most significant mathematical models for a financial market. In this paper, the homotopy perturbation method is combined with Mohand transform to obtain the approximate solution of the fractional Black-Scholes European option pricing equation. The fractional derivative is considered in the Caputo sense.
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STOCHASTIC BLACK-SCHOLES EQUATION WITH TIME-FRACTIONAL DERIVATIVE ON THE HALF-LINE [PDF]

International Journal of Pure and Apllied Mathematics, 2016
We investigate the pricing of options using a modified Black-Scholes equation with a time-fractional derivative and additive white noise on the half-line. We construct the Green function for the initial-boundary value problem adapting the main ideas of the Fokas method and we prove existence and uniqueness of solutions.
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Analytically pricing double barrier options based on a time-fractional Black–Scholes equation

Computers & Mathematics with Applications, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wen-Ting Chen, Xiang Xu, Song-Ping Zhu
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An interior penalty method for a parabolic complementarity problem involving a fractional Black-Scholes operator

Journal of Inequalities and Applications
In this paper, an interior penalty method is proposed to solve a parabolic complementarity problem involving fractional Black–Scholes operator arising in pricing American options under a geometric Lévy process.
Yarui Duan, Song Wang, Yuying Zhou, Leijun Zhu   +3 more
doaj   +1 more source

Exact Solution of Fractional Black-Scholes European Option Pricing Equations

Applied Mathematics, 2018
We introduce two algorithms in order to find the exact solution of the nonlinear Time-fractional Partial differential equation, in this research work. Those algorithms are proposed in the following structure: The Modified Homotopy Perturbation Method (MHPM), The Homotopy Perturbation and Sumudu Transform Method.
Maryeme Ouafoudi, Fei Gao
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Efficient High-Accuracy Numerical Scheme for the Solution of Time Fractional Parabolic Partial Differential Equations With Application in Financial Modeling

Journal of Mathematics
Parabolic partial equations, particularly the Black–Scholes equation, are fundamental in mathematical finance for option pricing and risk management. Despite their widespread use, efficiently solving these equations remains a challenge, especially in ...
Hadis Azin, Ali Iloon Kashkooly
doaj   +1 more source