Three local weak form meshless techniques to evaluate European and Bermudian options under Back&Sholes and jump-diffusion models

Recently, several numerical methods have been proposed for pricing option, but very few articles consider meshless methods; in this work the local weak form meshless methods are proposed for pricing European and Bermudian options under either Black&Sholes or Merton and Kou jump-diffusion models. The focus is on three schemes: the meshless local Petrov-Galerkin (MLPG), the local boundary integral equation (LBIE) methods, based on moving least square approximation (MLS), and the local radial point interpolation (LRPI) with Wendland’s compactly supported radial basis functions (WCS-RBFs). These schemes belong to the family of meshless methods, because a traditional non-overlapping, continuous mesh is not required, either for the construction of the shape function, or for the integration of the local subdomains. Numerical experiments are exhibited to analyze if the presented approaches are accurate and fast. The numerical results obtained using meshless methods are compared with the finite difference method, to investigate if these new methods are actually better then the classic one.