A new approach for pricing American put options

A new approach based on stochastic approximation is proposed for pricing American put options. Formulated as optimal stopping problems, the solutions of pricing American options are often given in terms of threshold values. Assuming that the market model includes a Markov regime switching as well as the usual geometric Brownian motion, we develop a stochastic approximation algorithm to approximate the threshold levels. We obtain convergence and rates of convergence by weak convergence methods, and report numerical experiments to demonstrate the effectiveness of the approach. The proposed approach provides us with a viable computational approach, and has distinctive advantage in terms of the reduced computational complexity compared with the optimal stopping approach.