A regression based smoothing spline Monte Carlo algorithm for pricing American options

Pricing of American options can be achieved by solving optimal stopping problems. This in turn can be done by computing so-called continuation values, which we represent as regression functions defined recursively by using the continuation values of the next time step. We use Monte Carlo to generate data and apply smoothing spline regression esti-mates to estimate the continuation values from these data. All parameters of the estimate are chosen data dependent. Results concerning consistency and rate of convergence of the estimates are presented. AMS classification: Primary 91B28, 60G40, 93E20; secondary 65C05, 93E24, 62G05. Key words and phrases: American options, consistency, nonparametric regression, optima