Numerical Approximation of Option Pricing Model Under Jump Diffusion Using the Laplace Transformation Method

Volume 8, Issue 4

H. Lee & D. Sheen

DOI:

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.

Keywords

Laplace inversion Option Derivative Jump-diffusion

AMS Subject Headings

91B02 44A10 35K50

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