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Volume 8, Issue 4
Convergence of Iterative Laplace Transform Methods for a System of Fractional PDEs and PIDEs Arising in Option Pricing

Zhiqiang Zhou, Jingtang Ma & Xuemei Gao

DOI: 10.4208/eajam.130218.290618

East Asian J. Appl. Math., 8 (2018), pp. 782-808.

Published online: 2018-10

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  • Abstract

Iterative Laplace transform methods for fractional partial differential equations and fractional partial integro-differential equations arising in European option pricing with the Lévy α-stable processes and regime-switching or state-dependent jump rates are studied and numerical contour integral methods to inverse the Laplace transform are developed. It is shown that the methods under consideration have the second-order convergence rate in space and spectral-order convergence for Laplace transform inversion.

  • Keywords

Fractional partial differential equation, option pricing regime-switching, Laplace transform method, convergence rate.

  • AMS Subject Headings

35R35, 91G20, 91G60, 91G80

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-8-782, author = {Zhiqiang Zhou, Jingtang Ma and Xuemei Gao}, title = {Convergence of Iterative Laplace Transform Methods for a System of Fractional PDEs and PIDEs Arising in Option Pricing}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {8}, number = {4}, pages = {782--808}, abstract = {

Iterative Laplace transform methods for fractional partial differential equations and fractional partial integro-differential equations arising in European option pricing with the Lévy α-stable processes and regime-switching or state-dependent jump rates are studied and numerical contour integral methods to inverse the Laplace transform are developed. It is shown that the methods under consideration have the second-order convergence rate in space and spectral-order convergence for Laplace transform inversion.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.130218.290618}, url = {http://global-sci.org/intro/article_detail/eajam/12819.html} }
TY - JOUR T1 - Convergence of Iterative Laplace Transform Methods for a System of Fractional PDEs and PIDEs Arising in Option Pricing AU - Zhiqiang Zhou, Jingtang Ma & Xuemei Gao JO - East Asian Journal on Applied Mathematics VL - 4 SP - 782 EP - 808 PY - 2018 DA - 2018/10 SN - 8 DO - http://doi.org/10.4208/eajam.130218.290618 UR - https://global-sci.org/intro/article_detail/eajam/12819.html KW - Fractional partial differential equation, option pricing KW - regime-switching, Laplace transform method, convergence rate. AB -

Iterative Laplace transform methods for fractional partial differential equations and fractional partial integro-differential equations arising in European option pricing with the Lévy α-stable processes and regime-switching or state-dependent jump rates are studied and numerical contour integral methods to inverse the Laplace transform are developed. It is shown that the methods under consideration have the second-order convergence rate in space and spectral-order convergence for Laplace transform inversion.

Zhiqiang Zhou, Jingtang Ma and Xuemei Gao. (2018). Convergence of Iterative Laplace Transform Methods for a System of Fractional PDEs and PIDEs Arising in Option Pricing. East Asian Journal on Applied Mathematics. 8 (4). 782-808. doi:10.4208/eajam.130218.290618
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