An RBF–FD method for pricing American options under jump–diffusion models

American option prices under jump–diffusion models are determined as solutions to partial integro-differential equations (PIDE). In this paper a new combination of a time and spatial discretization applied to a linear complementary formulation (LCP) of the free boundary PIDE is proposed. First a coo...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2018-11, Vol.76 (10), p.2434-2459
Main Authors: Haghi, Majid, Mollapourasl, Reza, Vanmaele, Michèle
Format: Article
Language:English
Subjects:
Basis functions
Conditioning
Differential equations
Discretization
Finite difference
Finite difference method
Free boundaries
Integration
Mathematical models
Matrix
Merton’s and Kou’s models
Option pricing
Radial basis function
Radial basis functions
Securities prices
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Summary:American option prices under jump–diffusion models are determined as solutions to partial integro-differential equations (PIDE). In this paper a new combination of a time and spatial discretization applied to a linear complementary formulation (LCP) of the free boundary PIDE is proposed. First a coordinate stretching transformation is performed to the asset price so that the computation of the prices can be focused on regions of real interest instead of on the whole solution domain. An implicit–explicit time discretization applied to the reformulated LCP on a uniform temporal grid is followed by a spatial discretization to get a fully discrete system. The radial basis function (RBF) finite difference method is a local method resulting in a sparse linear system in contrast to global RBF-methods which lead to ill-conditioned dense matrix systems. For the corresponding European option we prove consistency, stability and second-order convergence in a discrete L2-norm. We derive mild conditions for the model parameters under which these results hold. Numerical experiments are performed with European and American options, and a comparison with numerical results available in the literature illustrates the accuracy and efficiency of the proposed algorithm.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2018.08.040