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Volume 11, Issue 2
A Second Order Numerical Scheme for Fractional Option Pricing Models

Ling-Xi Zhang, Ren-Feng Peng & Jun-Feng Yin

East Asian J. Appl. Math., 11 (2021), pp. 326-348.

Published online: 2021-02

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  • Abstract

A number of fractional option models (FMLS, CGMY, KoBol) are proposed and studied under assumption that the motion of the underlying assets follows a Lévy process. Numerical methods for these option pricing models are based on solution of fractional partial differential equations. To discretise them, we employ a second order numerical scheme and study its stability and convergence. Numerical experiments show the efficiency of the method and its convergence. Simulations related to practical stock markets, further confirm the robustness of the scheme and show that KoBol model has advantage over the classical Black-Scholes model.

  • AMS Subject Headings

65M06, 65M12, 65M32, 91G60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-11-326, author = {Zhang , Ling-XiPeng , Ren-Feng and Yin , Jun-Feng}, title = {A Second Order Numerical Scheme for Fractional Option Pricing Models}, journal = {East Asian Journal on Applied Mathematics}, year = {2021}, volume = {11}, number = {2}, pages = {326--348}, abstract = {

A number of fractional option models (FMLS, CGMY, KoBol) are proposed and studied under assumption that the motion of the underlying assets follows a Lévy process. Numerical methods for these option pricing models are based on solution of fractional partial differential equations. To discretise them, we employ a second order numerical scheme and study its stability and convergence. Numerical experiments show the efficiency of the method and its convergence. Simulations related to practical stock markets, further confirm the robustness of the scheme and show that KoBol model has advantage over the classical Black-Scholes model.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.020820.121120}, url = {http://global-sci.org/intro/article_detail/eajam/18637.html} }
TY - JOUR T1 - A Second Order Numerical Scheme for Fractional Option Pricing Models AU - Zhang , Ling-Xi AU - Peng , Ren-Feng AU - Yin , Jun-Feng JO - East Asian Journal on Applied Mathematics VL - 2 SP - 326 EP - 348 PY - 2021 DA - 2021/02 SN - 11 DO - http://doi.org/10.4208/eajam.020820.121120 UR - https://global-sci.org/intro/article_detail/eajam/18637.html KW - Lévy process, fractional partial differential equation, option pricing, finite difference, stock index option. AB -

A number of fractional option models (FMLS, CGMY, KoBol) are proposed and studied under assumption that the motion of the underlying assets follows a Lévy process. Numerical methods for these option pricing models are based on solution of fractional partial differential equations. To discretise them, we employ a second order numerical scheme and study its stability and convergence. Numerical experiments show the efficiency of the method and its convergence. Simulations related to practical stock markets, further confirm the robustness of the scheme and show that KoBol model has advantage over the classical Black-Scholes model.

Ling-Xi Zhang, Ren-Feng Peng & Jun-Feng Yin. (2021). A Second Order Numerical Scheme for Fractional Option Pricing Models. East Asian Journal on Applied Mathematics. 11 (2). 326-348. doi:10.4208/eajam.020820.121120
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