Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 318, Issue -, Pages 79-92Publisher
ELSEVIER
DOI: 10.1016/j.cam.2016.11.038
Keywords
European option pricing; American option pricing; Merton's jump-diffusion model; Finite difference methods; Discontinuous Galerkin finite element methods; Multigrid methods
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Funding
- Natural Science Foundation of China [11371074]
- Hunan Provincial Natural Science Foundation of China [13JJ1020]
- Research Foundation of Education Bureau of Hunan Province, China [13A108]
- Open Fund Project of Key Research Institute of Philosophies and Social Sciences in Hunan Universities
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In this paper, we consider discontinuous Galerkin (DG) finite element together with finite difference (FD) scheme for solving Merton's jump-diffusion model, which is given by a partial integro-differential equations (PIDEs). Spatial differential operators are discretized using FD on a uniform grid, and time stepping is performed using the DG finite element method. The treatment of the integral term associated with jumps in models is more challenging. The discretization of this integral term will lead to full matrices for the non-locality of the integral operator. To fast solve this model, multigrid method is used for solving such linear algebraical system. Numerical comparison of multigrid method and GMRES method shows that multigrid method is superior to and more effective than GMRES method in solving the dense algebraic systems resulting from the FD approximations of the PIDEs. (C) 2016 Elsevier B.V. All rights reserved.
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