Regression methods in pricing American and Bermudan options using consumption processes

Abstract

Numerical algorithms for efficient pricing multidimensional discrete-time American and Bermudan options are constructed using regression methods and a new approach for computing upper bounds of the options' price. Using the sample space with payoffs at the optimal stopping times, we propose sequential estimates for continuation values, values of the consumption process, and stopping times on the sample paths. The approach allows constructing both lower and upper bounds for the price by Monte Carlo simulations. The algorithms are tested by pricing Bermudan max-calls and swaptions in the Libor market model.