An efficient hybrid penalty method for pricing American options

We propose a hybrid numerical method for computing the prices of American options. In order to solve efficiently and accurately the linear complementarity problem arising in the valuation of American options, the proposed method initially applies the penalty method to annihilate the nonlinear error from the free boundary, then performs the θ-method with projection to solve the rest of the problem quickly. Numerical computations show that the proposed hybrid method is more efficient than other existing methods for a given level of accuracy.