Qualitatively stable nonstandard finite difference scheme for numerical solution of the nonlinear Black-Scholes equation
type: Item
instance of: scholarly article
title: Qualitatively stable nonstandard finite difference scheme for numerical solution of the nonlinear Black-Scholes equation
zbMATH Open document ID: 1477.91060
DOI: 10.1155/2021/6679484
author: Yanyan Li
published in: Journal of Mathematics
publication date: 2021-06-28T00:00:00Z
review text: Summary: In this paper, we use a numerical method for solving the nonlinear Black-Scholes partial differential equation of the European option under transaction costs, which is based on the nonstandard discretization of the spatial derivatives. The proposed scheme, in addition to the unconditional positivity, is stable, consistent, and monotone. In order to illustrate the efficiency of the new method, numerical results have been performed by four models.
Mathematics Subject Classification ID: 91G60
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 91G20
Mathematics Subject Classification ID: 35Q91
zbMATH DE Number: 7363836
Wikidata QID: Q113268332
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/6679484
OpenAlex ID: W3163627781
cites work: Q4905685
cites work: On the risk-adjusted pricing-methodology-based valuation of vanilla options and explanation of the volatility smile
cites work: An upwind finite difference method for a nonlinear Black-Scholes equation governing European option valuation under transaction costs
cites work: A numerical method for European option pricing with transaction costs nonlinear equation
cites work: A positivity-preserving numerical scheme for nonlinear option pricing models
cites work: Q5233632
cites work: Q5233631
cites work: Q4959145
cites work: The homotopy perturbation method for the Black–Scholes equation
cites work: Homotopy perturbation method: a new nonlinear analytical technique
cites work: Variational iteration method: New development and applications
cites work: Q5415415
cites work: Q2945121
cites work: High Order Compact Finite Difference Schemes for a Nonlinear Black-Scholes Equation
cites work: Numerical Methods for Non-Linear Black–Scholes Equations
cites work: Fast computational approach to the delta Greek of non-linear Black-Scholes equations
cites work: Approximate solution of nonlinear Black-Scholes equation via a fully discretized fourth-order method
cites work: Q4309510
cites work: Q2951725
cites work: A positive and elementary stable nonstandard explicit scheme for a mathematical model of the influenza disease
cites work: Numerical solution of linear and nonlinear Black-Scholes option pricing equations
cites work: An improvement on the positivity results for 2-stage explicit Runge-Kutta methods
cites work: Q4647038
cites work: Q3000773
cites work: Q3000764
cites work: Numerical valuation of discrete double barrier options
cites work: Qualitatively stability of nonstandard 2-stage explicit Runge-Kutta methods of order two
cites work: A new positivity‐preserving nonstandard finite difference scheme for the DWE
cites work: A positivity‐preserving nonstandard finite difference scheme for the damped wave equation
cites work: Efficient implicit scheme with positivity preserving and smoothing properties
description: scientific article; zbMATH DE number 7363836