Numerical Approximation of Option Pricing Model Under Jump Diffusion Using the Laplace Transformation Method
Year: 2011
International Journal of Numerical Analysis and Modeling, Vol. 8 (2011), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2011-IJNAM-701
International Journal of Numerical Analysis and Modeling, Vol. 8 (2011), Iss. 4 : pp. 566–583
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Laplace inversion Option Derivative Jump-diffusion.