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In this paper we develop two novel numerical methods for the partial integral differential equation arising from the valuation of an option whose underlying asset is governed by a jump diffusion process. These methods are based on a fitted finite volume method for the spatial discretization, an implicit-explicit time stepping scheme and the Crank-Nicolson time stepping method. We show that the discretization methods are unconditionally stable in time and the system matrices of the resulting linear systems are M-matrices. The resulting linear systems involve products of a dense matrix and vectors and an Fast Fourier Transformation (FFT) technique is used for the evaluation of these products. Furthermore, a splitting technique is proposed for the solution of the discretized system arising from the Crank-Nicolson scheme. Numerical results are presented to show the rates of convergence and the robustness of the numerical method.
}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/758.html} }In this paper we develop two novel numerical methods for the partial integral differential equation arising from the valuation of an option whose underlying asset is governed by a jump diffusion process. These methods are based on a fitted finite volume method for the spatial discretization, an implicit-explicit time stepping scheme and the Crank-Nicolson time stepping method. We show that the discretization methods are unconditionally stable in time and the system matrices of the resulting linear systems are M-matrices. The resulting linear systems involve products of a dense matrix and vectors and an Fast Fourier Transformation (FFT) technique is used for the evaluation of these products. Furthermore, a splitting technique is proposed for the solution of the discretized system arising from the Crank-Nicolson scheme. Numerical results are presented to show the rates of convergence and the robustness of the numerical method.