Year: 2018
Communications in Computational Physics, Vol. 24 (2018), Iss. 2 : pp. 531–556
Abstract
Using the idea of weighted and shifted differences, we propose a novel finite difference formula with second-order accuracy for the tempered fractional derivatives. For tempered fractional diffusion equations, the proposed finite difference formula yields an unconditionally stable scheme when an implicit Euler method is used. For the numerical simulation and as an application, we take the CGMYe model as an example. The numerical experiments show that second-order accuracy is achieved for both European and American options.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2018-0001
Communications in Computational Physics, Vol. 24 (2018), Iss. 2 : pp. 531–556
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Tempered fractional derivatives fractional differential equations method of characteristics CGMYe model.