Approximate solution of nonlinear Black–Scholes equation via a fully discretized fourth-order method

In this work, a new fourth-order finite difference (FD) approximation (for both structured and unstructured grid of nodes) is contributed and equipped with the fourth-order Runge–Kutta scheme to tackle the financial nonlinear partial differential equation (PDE) of Black–Scholes. This timedependent P...

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Bibliographic Details
Published inAIMS mathematics Vol. 5; no. 2; pp. 879 - 893
Main Authors Ghanadian, Azadeh, Lotfi, Taher
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2020
Subjects
black-scholes equation
fd weights
fourth-order
time-dependent
transaction costs
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Summary:In this work, a new fourth-order finite difference (FD) approximation (for both structured and unstructured grid of nodes) is contributed and equipped with the fourth-order Runge–Kutta scheme to tackle the financial nonlinear partial differential equation (PDE) of Black–Scholes. This timedependent PDE problem is converted to a set of ordinary differential equations (ODEs). It is proved that under several criteria the procedure is time stable. Computational illustrations presented here, show that our approach is fast and accurate. The proposed technique reduces the computational cost, when more accurate results are requested.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2020060