A quasi-radial basis functions method for American options pricing

Based on the idea of quasi-interpolation and radial basis functions approximation, a fast and accurate numerical method is developed for solving the Black-Scholes equation for valuation of American options prices. Since the method does not require solving a resultant full matrix, the ill-conditioning problem resulting from using the radial basis functions as a global interpolant can be avoided. The method has been shown to be effective in solving problems with free boundary condition. As indicated in the numerical computation for the American option pricing, an excellent approximation of the solution as well as the free optimal exercise boundary can be obtained.