Efficient meshfree method for pricing European and American put options on a non-dividend paying asset

Abstract

We develop efficient meshfree method based on radial basis functions (RBFs) to solve European and American option pricing problems arising in computational finance. The application of RBFs leads to system of differential equations which are then solved by a time integration θ -method. The main difficulty in pricing the American options lies in the fact that these options are allowed to be exercised at any time before their expiry. Such an early exercise right purchased by the holder of the option results into a free boundary problem. Following the approach of Nielsen et al. [B.F. Nielsen, O. Skavhaug and A. Tveito, Penalty methods for the numerical solution of American multi-asset option problems. J. Comput. Appl. Math. 222, 3-16 (2008)], we use a small penalty term to remove the free boundary. The method is analyzed for stability. Numerical results describing the payoff functions and option values are also present. We also compute the two important Greeks, delta and gamma, of these options.