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Volume 36, Issue 4
Modified Differential Transform Method for Solving Black-Scholes Pricing Model of European Option Valuation Paying Continuous Dividends

Manzoor Ahmad, Raishree Mishra & Renu Jain

DOI: 10.4208/jpde.v36.n4.4

J. Part. Diff. Eq., 36 (2023), pp. 381-393.

Published online: 2023-11

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  • Abstract

Option pricing is a major problem in quantitative finance. The Black-Scholes model proves to be an effective model for the pricing of options. In this paper a computational method known as the modified differential transform method has been employed to obtain the series solution of Black-Scholes equation with boundary conditions for European call and put options paying continuous dividends. The proposed method does not need discretization to find out the solution and thus the computational work is reduced considerably. The results are plotted graphically to establish the accuracy and efficacy of the proposed method.

  • Keywords

European option pricing, Black-Scholes equation, call option, put option, modified differential transform method.

  • AMS Subject Headings

91G20, 91G30, 91G80, 35Q91

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-36-381, author = {Ahmad , ManzoorMishra , Raishree and Jain , Renu}, title = {Modified Differential Transform Method for Solving Black-Scholes Pricing Model of European Option Valuation Paying Continuous Dividends}, journal = {Journal of Partial Differential Equations}, year = {2023}, volume = {36}, number = {4}, pages = {381--393}, abstract = {

Option pricing is a major problem in quantitative finance. The Black-Scholes model proves to be an effective model for the pricing of options. In this paper a computational method known as the modified differential transform method has been employed to obtain the series solution of Black-Scholes equation with boundary conditions for European call and put options paying continuous dividends. The proposed method does not need discretization to find out the solution and thus the computational work is reduced considerably. The results are plotted graphically to establish the accuracy and efficacy of the proposed method.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v36.n4.4}, url = {http://global-sci.org/intro/article_detail/jpde/22135.html} }
TY - JOUR T1 - Modified Differential Transform Method for Solving Black-Scholes Pricing Model of European Option Valuation Paying Continuous Dividends AU - Ahmad , Manzoor AU - Mishra , Raishree AU - Jain , Renu JO - Journal of Partial Differential Equations VL - 4 SP - 381 EP - 393 PY - 2023 DA - 2023/11 SN - 36 DO - http://doi.org/10.4208/jpde.v36.n4.4 UR - https://global-sci.org/intro/article_detail/jpde/22135.html KW - European option pricing, Black-Scholes equation, call option, put option, modified differential transform method. AB -

Option pricing is a major problem in quantitative finance. The Black-Scholes model proves to be an effective model for the pricing of options. In this paper a computational method known as the modified differential transform method has been employed to obtain the series solution of Black-Scholes equation with boundary conditions for European call and put options paying continuous dividends. The proposed method does not need discretization to find out the solution and thus the computational work is reduced considerably. The results are plotted graphically to establish the accuracy and efficacy of the proposed method.

Manzoor Ahmad, Raishree Mishra & Renu Jain. (2023). Modified Differential Transform Method for Solving Black-Scholes Pricing Model of European Option Valuation Paying Continuous Dividends. Journal of Partial Differential Equations. 36 (4). 381-393. doi:10.4208/jpde.v36.n4.4
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