Valuation of American Options with Meshfree Methods

In this paper, we price American options using the radial basis function (RBF) interpolation method. Two processes for the volatility are assumed: local volatility and stochastic volatility. In particular, we focus on the constant elasticity of variance (CEV) model (Cox and Ross (1976)) and the Heston model (Heston (1993)). Several experiments are performed to evaluate the pricing accuracy and the computational efficiency of the RBF method. The results are compared against solutions obtained by two traditional techniques in finance, namely the standard finite difference method (FDM) and the Monte Carlo simulation (MCS). The option prices approximated by the RBF interpolation are also contrasted with the results reported in other recent studies. The findings show that the RBF interpolation provides accurate and efficient option prices under the two volatility processes under investigation. In particular, the gains of using the meshfree method are observed in the Heston model due to its two-dimensional setting. Under the CEV model, the performance of the RBF method is similar to the FDM, but superior compared with the MCS. Under the Heston model specification, the RBF method outperforms both the FDM and the MCS.