PostprintThis is the accepted version of a paper published in Computers and Mathematics with Applications. This paper has been peer-reviewed but does not include the final publisher proof-corrections or journal pagination.Citation for the original published paper (version of record):Shcherbakov, V., Larsson, E. (2016) Radial basis function partition of unity methods for pricing vanilla basket options. Abstract Mesh-free methods based on radial basis function (RBF) approximation are becoming widely used for solving PDE problems. They are flexible with respect to the problem geometry and highly accurate. A disadvantage of these methods is that the linear system to be solved becomes dense for globally supported RBFs. A remedy is to introduce localisation techniques such as partition of unity. RBF partition of unity methods (RBF-PUM) allow for a significant sparsification of the linear system and lower the computational effort. In this work we apply a global RBF method as well as RBF-PUM to problems in option pricing. We consider one-and two-dimensional vanilla options. In order to price American options we employ a penalty approach. A penalty term, suitable for American multi-asset call options, has been designed. RBF-PUM is shown to be competitive compared with a finite difference method and a global RBF method. It is as accurate as the global RBF method, but significantly faster. The results for RBF-PUM look promising for extension to higher-dimensional problems.
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