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Lie symmetry, exact solutions and conservation laws of bi-fractional Black–Scholes equation derived by the fractional G-Brownian motion

International Journal of Financial Engineering, 2023
The Black–Scholes equation is an important analytical tool for option pricing in finance. This paper discusses the Lie symmetry analysis of bi-fractional Black–Scholes equation derived by the fractional G-Brownian motion.
Jicheng Yu, Yuqiang Feng, Xianjia Wang
semanticscholar   +1 more source

Lie symmetry analysis and exact solutions of time fractional Black–Scholes equation

International Journal of Financial Engineering, 2022
The Black–Scholes equation is an important analytical tool for option pricing in finance. This paper discusses the constructive methods of exact solutions to time fractional Black–Scholes equation.
Jicheng Yu, Yuqiang Feng, Xianjia Wang
semanticscholar   +1 more source

A high accuracy numerical method and its convergence for time-fractional Black-Scholes equation governing European options

, 2020
This paper is concerned with the design of a high order numerical approach based on a uniform mesh for efficient numerical solution of time-fractional Black-Scholes equation, governing European options.
P. Roul
semanticscholar   +1 more source

On modified Black–Scholes equation

Chaos, Solitons & Fractals, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ahmed, E., Abdusalam, H. A.
openaire   +1 more source

Generalized heat diffusion equations with variable coefficients and their fractalization from the Black-Scholes equation

Communications in Theoretical Physics, 2021
In this study, we prove that modified diffusion equations, including the generalized Burgers’ equation with variable coefficients, can be derived from the Black-Scholes equation with a time-dependent parameter based on the propagator method known in ...
R. El-Nabulsi, A. Golmankhaneh
semanticscholar   +1 more source

Symmetry Breaking for Black–Scholes Equations

Communications in Theoretical Physics, 2007
Summary: Black-Scholes equation is used to model stock option pricing. In this paper, optimal systems with one to four parameters of Lie point symmetries for Black-Scholes equation and its extension are obtained. Their symmetry breaking interaction associated with the optimal systems is also studied.
Yang, Xuan-Liu   +2 more
openaire   +1 more source

Homotopy analysis method and its applications in the valuation of European call options with time-fractional Black-Scholes equation

, 2020
This paper presents the applications of Homotopy Analysis Method (HAM) in the valuation of a European Call Option (ECO) with Time-Fractional Black-Scholes Equation (TFBSE). The fractional derivative is considered in the sense of Caputo.
Sunday Emmanuel Fadugba
semanticscholar   +1 more source

Recovery of the time-dependent implied volatility of time fractional Black–Scholes equation using linearization technique

, 2021
This paper tries to examine the recovery of the time-dependent implied volatility coefficient from market prices of options for the time fractional Black–Scholes equation (TFBSM) with double barriers option.
S. Iqbal, Yujie Wei
semanticscholar   +1 more source

A Compact Difference Scheme for Mixed‐Type Time‐Fractional Black‐Scholes Equation in European Option Pricing

Mathematical methods in the applied sciences
The time‐fractional Black‐Scholes equation (TFBSE) is an important model in financial markets, widely used for estimating the prices of European options under conditions of memory effects and anomalous diffusion.
Jiawei Wang   +3 more
semanticscholar   +1 more source

On the numerical solution of time fractional Black-Scholes equation

International Journal of Computational Mathematics, 2021
In this study, we provide a numerical method to approximate the solution of the time fractional Black-Sholes equation by applying the multiquadric (MQ) quasi-interpolation scheme and the integrated radial basis function networks scheme.
M. Sarboland, A. Aminataei
semanticscholar   +1 more source

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