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Volume 6, Issue 4
Laplace Transformation Method for the Black-Scholes Equation

H. Lee & D. Sheen

Int. J. Numer. Anal. Mod., 6 (2009), pp. 642-658.

Published online: 2009-06

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  • Abstract

In this paper we apply the innovative Laplace transformation method introduced by Sheen, Sloan, and Thomée (IMA J. Numer. Anal., 2003) to solve the Black-Scholes equation. The algorithm is of arbitrary high convergence rate and naturally parallelizable. It is shown that the method is very efficient for calculating various option prices. Existence and uniqueness properties of the Laplace transformed Black-Scholes equation are analyzed. Also a transparent boundary condition associated with the Laplace transformation method is proposed. Several numerical results for various options under various situations confirm the efficiency, convergence and parallelization property of the proposed scheme.

  • Keywords

Black-Scholes equation, basket option, Laplace inversion, parallel method, transparent boundary condition.

  • AMS Subject Headings

91B02, 44A10, 35K50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-6-642, author = {H. Lee and D. Sheen}, title = {Laplace Transformation Method for the Black-Scholes Equation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2009}, volume = {6}, number = {4}, pages = {642--658}, abstract = {

In this paper we apply the innovative Laplace transformation method introduced by Sheen, Sloan, and Thomée (IMA J. Numer. Anal., 2003) to solve the Black-Scholes equation. The algorithm is of arbitrary high convergence rate and naturally parallelizable. It is shown that the method is very efficient for calculating various option prices. Existence and uniqueness properties of the Laplace transformed Black-Scholes equation are analyzed. Also a transparent boundary condition associated with the Laplace transformation method is proposed. Several numerical results for various options under various situations confirm the efficiency, convergence and parallelization property of the proposed scheme.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/789.html} }
TY - JOUR T1 - Laplace Transformation Method for the Black-Scholes Equation AU - H. Lee & D. Sheen JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 642 EP - 658 PY - 2009 DA - 2009/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/789.html KW - Black-Scholes equation, basket option, Laplace inversion, parallel method, transparent boundary condition. AB -

In this paper we apply the innovative Laplace transformation method introduced by Sheen, Sloan, and Thomée (IMA J. Numer. Anal., 2003) to solve the Black-Scholes equation. The algorithm is of arbitrary high convergence rate and naturally parallelizable. It is shown that the method is very efficient for calculating various option prices. Existence and uniqueness properties of the Laplace transformed Black-Scholes equation are analyzed. Also a transparent boundary condition associated with the Laplace transformation method is proposed. Several numerical results for various options under various situations confirm the efficiency, convergence and parallelization property of the proposed scheme.

H. Lee and D. Sheen. (2009). Laplace Transformation Method for the Black-Scholes Equation. International Journal of Numerical Analysis and Modeling. 6 (4). 642-658. doi:
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