Standard

Fast numerical scheme for the time-fractional option pricing model with asset-price-dependent variable order. / Zhang, Meihui; Jia, Jinhong; Hendy, Ahmed et al.
In: Applied Numerical Mathematics, No. 192, 10.2023, p. 414-430.

Research output: Contribution to journal › Article › peer-review

Harvard

Zhang, M, Jia, J, Hendy, A, Zaky, M & Zheng, X 2023, 'Fast numerical scheme for the time-fractional option pricing model with asset-price-dependent variable order', Applied Numerical Mathematics, no. 192, pp. 414-430. https://doi.org/10.1016/j.apnum.2023.06.014

APA

Zhang, M., Jia, J., Hendy, A., Zaky, M., & Zheng, X. (2023). Fast numerical scheme for the time-fractional option pricing model with asset-price-dependent variable order. Applied Numerical Mathematics, (192), 414-430. https://doi.org/10.1016/j.apnum.2023.06.014

Vancouver

Zhang M, Jia J, Hendy A, Zaky M, Zheng X. Fast numerical scheme for the time-fractional option pricing model with asset-price-dependent variable order. Applied Numerical Mathematics. 2023 Oct;(192):414-430. doi: 10.1016/j.apnum.2023.06.014

Author

Zhang, Meihui ; Jia, Jinhong ; Hendy, Ahmed et al. / Fast numerical scheme for the time-fractional option pricing model with asset-price-dependent variable order. In: Applied Numerical Mathematics. 2023 ; No. 192. pp. 414-430.

BibTeX

@article{532f733c1bb64786b6102707f4c973f0,
title = "Fast numerical scheme for the time-fractional option pricing model with asset-price-dependent variable order",
abstract = "We provide a fast numerical technique for a time-fractional option pricing model with asset-price-dependent variable order. Due to the complicated variable-order fractional derivative and its related fast approximations, the temporal coefficients are coupled with the inner product of the finite element method and lose monotonicity, which introduces uncommon difficulties in numerical analysis. In addition, the Riemann-Liouville fractional operators are often used in option pricing models, but its variable-order case gets far less attention than the corresponding Caputo-type problems. We prove error estimates for the proposed fast method and show that the computational cost is almost linear with respect to the temporal steps, which is much faster than the quadratic growth of the time-stepping solver. Numerical experiments are performed to illustrate the theoretical findings.",
author = "Meihui Zhang and Jinhong Jia and Ahmed Hendy and Mahmoud Zaky and Xiangcheng Zheng",
note = "The authors are grateful to the anonymous referees for their constructive feedback and helpful suggestions, which highly improved the paper. This work was partially funded by the National Social Science Foundation of China under Grant 20CTJ002 and the National Natural Science Foundation of China under Grant 12001337 . Ahmed S. Hendy wishes to acknowledge the support of the RSF grant, project 22-21-00075.",
year = "2023",
month = oct,
doi = "10.1016/j.apnum.2023.06.014",
language = "English",
pages = "414--430",
journal = "Applied Numerical Mathematics",
issn = "0168-9274",
publisher = "Elsevier",
number = "192",

}

RIS

TY - JOUR

T1 - Fast numerical scheme for the time-fractional option pricing model with asset-price-dependent variable order

AU - Zhang, Meihui

AU - Jia, Jinhong

AU - Hendy, Ahmed

AU - Zaky, Mahmoud

AU - Zheng, Xiangcheng

N1 - The authors are grateful to the anonymous referees for their constructive feedback and helpful suggestions, which highly improved the paper. This work was partially funded by the National Social Science Foundation of China under Grant 20CTJ002 and the National Natural Science Foundation of China under Grant 12001337 . Ahmed S. Hendy wishes to acknowledge the support of the RSF grant, project 22-21-00075.

PY - 2023/10

Y1 - 2023/10

N2 - We provide a fast numerical technique for a time-fractional option pricing model with asset-price-dependent variable order. Due to the complicated variable-order fractional derivative and its related fast approximations, the temporal coefficients are coupled with the inner product of the finite element method and lose monotonicity, which introduces uncommon difficulties in numerical analysis. In addition, the Riemann-Liouville fractional operators are often used in option pricing models, but its variable-order case gets far less attention than the corresponding Caputo-type problems. We prove error estimates for the proposed fast method and show that the computational cost is almost linear with respect to the temporal steps, which is much faster than the quadratic growth of the time-stepping solver. Numerical experiments are performed to illustrate the theoretical findings.

AB - We provide a fast numerical technique for a time-fractional option pricing model with asset-price-dependent variable order. Due to the complicated variable-order fractional derivative and its related fast approximations, the temporal coefficients are coupled with the inner product of the finite element method and lose monotonicity, which introduces uncommon difficulties in numerical analysis. In addition, the Riemann-Liouville fractional operators are often used in option pricing models, but its variable-order case gets far less attention than the corresponding Caputo-type problems. We prove error estimates for the proposed fast method and show that the computational cost is almost linear with respect to the temporal steps, which is much faster than the quadratic growth of the time-stepping solver. Numerical experiments are performed to illustrate the theoretical findings.

UR - http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=85165226510

UR - https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=tsmetrics&SrcApp=tsm_test&DestApp=WOS_CPL&DestLinkType=FullRecord&KeyUT=001045905400001

U2 - 10.1016/j.apnum.2023.06.014

DO - 10.1016/j.apnum.2023.06.014

M3 - Article

SP - 414

EP - 430

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

SN - 0168-9274

IS - 192

ER -

ID: 43264880