Volume 8, Issue 4
Numerical Approximation of Option Pricing Model Under Jump Diffusion Using the Laplace Transformation Method

Int. J. Numer. Anal. Mod., 8 (2011), pp. 566-583.

Published online: 2011-08

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• Abstract

We propose a LT (Laplace transformation) method for solving the PIDE (partial integro-differential equation) arising from the financial mathematics. An option model under a jump-diffusion process is given by a PIDE, whose non-local integral term requires huge computational costs. In this work, the PIDE is transformed into a set of complex-valued elliptic problems by taking the Laplace transformation in time variable. Only a small number of Laplace transformed equations are then solved on a suitable choice of contour. Then the time-domain solution can be obtained by taking the Laplace inversion based on the chosen contour. Especially a splitting method is proposed to solve the PIDE, and its solvability and convergence are proved. Numerical results are shown to confirm the efficiency of the proposed method and the parallelizable property.

• AMS Subject Headings

91B02, 44A10, 35K50

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-8-566, author = {}, title = {Numerical Approximation of Option Pricing Model Under Jump Diffusion Using the Laplace Transformation Method}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2011}, volume = {8}, number = {4}, pages = {566--583}, abstract = {

We propose a LT (Laplace transformation) method for solving the PIDE (partial integro-differential equation) arising from the financial mathematics. An option model under a jump-diffusion process is given by a PIDE, whose non-local integral term requires huge computational costs. In this work, the PIDE is transformed into a set of complex-valued elliptic problems by taking the Laplace transformation in time variable. Only a small number of Laplace transformed equations are then solved on a suitable choice of contour. Then the time-domain solution can be obtained by taking the Laplace inversion based on the chosen contour. Especially a splitting method is proposed to solve the PIDE, and its solvability and convergence are proved. Numerical results are shown to confirm the efficiency of the proposed method and the parallelizable property.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/701.html} }
TY - JOUR T1 - Numerical Approximation of Option Pricing Model Under Jump Diffusion Using the Laplace Transformation Method JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 566 EP - 583 PY - 2011 DA - 2011/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/701.html KW - Laplace inversion, Option, Derivative, Jump-diffusion. AB -

We propose a LT (Laplace transformation) method for solving the PIDE (partial integro-differential equation) arising from the financial mathematics. An option model under a jump-diffusion process is given by a PIDE, whose non-local integral term requires huge computational costs. In this work, the PIDE is transformed into a set of complex-valued elliptic problems by taking the Laplace transformation in time variable. Only a small number of Laplace transformed equations are then solved on a suitable choice of contour. Then the time-domain solution can be obtained by taking the Laplace inversion based on the chosen contour. Especially a splitting method is proposed to solve the PIDE, and its solvability and convergence are proved. Numerical results are shown to confirm the efficiency of the proposed method and the parallelizable property.

H. Lee & D. Sheen. (1970). Numerical Approximation of Option Pricing Model Under Jump Diffusion Using the Laplace Transformation Method. International Journal of Numerical Analysis and Modeling. 8 (4). 566-583. doi:
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