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


Numerical approximation of option pricing model under jump diffusion using the Laplace transformation method

H. Lee 1, D. Sheen 2

1 Interdisciplinary Program in Computational Science and Technology, Seoul National University, Seoul 151-747, Korea. Current address: Bell Labs Seoul, 7th floor DMC R&D Center, Seoul 120¡V270, Korea.
2 Department of Mathematics, and Interdisciplinary Program in Computational Science and Technology, Seoul National University, Seoul 151-747, Korea.

Received by the editors February 10, 2011.
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 classifications: 91B02, 44A10, 35K50
Key words: Laplace inversion, Option, Derivative, Jump-diffusion.
 

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