RBF-PU method for pricing options under the jump–diffusion model with local volatility

摘要

Meshfree methods based on radial basis functions (RBFs) are of general interest for solving partial differential equations (PDEs) because they can provide high order or spectral convergence for smooth solutions in complex geometries. For global RBF methods, one of the major disadvantages is the computational cost associated with the dense linear systems that arise. Therefore, this paper is currently directed toward localized RBF approximations known as the RBF partition of unity (RBF-PU) method for partial integro-differential equation (PIDE) arisen in option pricing problems in jump–diffusion model. RBF-PU method produces algebraic systems with sparse matrices which have small condition number. Also, for comparison, some stable time discretization schemes are combined with the operator splitting method to get a fully discrete problem. Numerical examples are presented to illustrate the convergence and stability of the proposed algorithms for pricing European and American options with Merton and Kou models.