Error and stability estimates of a time-fractional option pricing model under fully spatial–temporal graded meshes

To price vanilla European and American options via the fractional Black–Scholes model, first a (2−α)-order discretization scheme for the Caputo fractional derivative based upon graded meshes along time is presented. This is fruitful for problems having nonsmooth data at the initial time. Second, a n...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 425; p. 115075
Main Authors Soleymani, Fazlollah, Zhu, Shengfeng
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.06.2023
Subjects
Caputo fractional derivative
Convergence analysis
Graded mesh
Memory
Option pricing
Radial basis function
Radial basis function
C63
Graded mesh
Option pricing
Memory
35R11
65M22
91B74
Caputo fractional derivative
Convergence analysis
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Summary:To price vanilla European and American options via the fractional Black–Scholes model, first a (2−α)-order discretization scheme for the Caputo fractional derivative based upon graded meshes along time is presented. This is fruitful for problems having nonsmooth data at the initial time. Second, a nonuniform discretization of space is also considered and the coefficient weights based upon meshless radial basis function generated finite difference (RBF-FD) methodology are contributed under the inverse quadratic function. The fully space–time nonuniform solution method is then constructed via the presented discretization formulas. Numerical tests are given to show effectiveness and accuracy of our numerical scheme.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2023.115075