An irregular grid approach for pricing high-dimensional American options ?

We propose and test a new method for pricing American options in a high-dimensional setting. The method is centred around the approximation of the associated complementarity problem on an irregular grid. We approximate the partial differential operator on this grid by appealing to the SDE representation of the underlying process and computing the root of the transition probability matrix of an approximating Markov chain. Experimental results in five dimensions are presented for four different payoff functions.