Pricing and hedging high-dimensional American options: an irregular grid approach

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 variational inequality on an irregular grid. We approximate the partial differential operator on this grid by appealing to the SDE representation of the stock process and computing the logarithm of the transition probability matrix of an approximating Markov chain. The option price is computed as a function of the underlyings, thus allowing for computation of deltas. The results of numerical tests in five dimensions are promising.