TY - JOUR
T1 - Numerical Approximation of Option Pricing Model Under Jump Diffusion Using the Laplace Transformation Method
AU - H. Lee & D. Sheen
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 - <p style="text-align: justify;">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.</p>