In this paper we introduce a new methodology to price American put options under stochastic interest rates. The method is a combination of an analytic approach and a binomial tree approach. We construct a binomial tree for the forward risk adjusted tree and calculate analytically the expected early exercise value in each point. For American puts with stochastic interest rates the correlation between the stock price process has different influences on the European option values and the early exercise premiums. This results in a nonmonotonic relation between this correlation and the American put option value. Furthermore, there is evidence that the early exercise premium due to stochastic interest rates is much larger than established before by other researchers
