Pricing American options with the SABR model

We introduce a simple and flexible method to price derivative securities on assets with volatilities which are stochastic. As a special case we treat the SABR model in more detail. Our approach is based on the construction of recombining trees using interpolation methods on probability measures, and this makes it very suitable for the application of parallel computing techniques. We show how one can easily incorporate features which are characteristic for practical option pricing problems, such as a term structure of interest, early exercise possibilities and the payment of cash dividends.