RESEARCH ARTICLE Meshfree Methods in Option Pricing

A meshfree approximation scheme based on the radial basis function methods is presented for the numerical solution of the options pricing model. This work deals with the valuation of the European, Barrier, Asian, American options of a single asset and American options of multi assets. The option prices are modeled by the Black-Scholes equation. The θ-method is used to discretize the equation with respect to time. By the next step, the option price is approximated in space with radial basis functions (RBF), in particular, we consider multiquadric radial basis functions (MQ-RBF). In case of American options a penalty method is used, i.e. the free boundary is removed by adding a small and continuous penalty term to the Black-Scholes equation. Finally, we present a comparison of analytical and finite difference solutions and numerical results.