ABSTRACT
This chapter is dedicated to the pricing and hedging of American options. This is a typical nonlinear problem that cannot be solved by the standard Monte Carlo method. American-style options were introduced in Section 5.1. We recall the theory of the valuation of American options, and then review numerical methods, with a particular focus on Monte Carlo methods, which are unavoidable when the number of variables exceeds three.1 We also cover chooser options, a generalization of American options in which the stopping times can be multiple. Primal and dual methods are illustrated by concrete numerical examples of option pricing: a multi-asset convertible bond, the restrikable put, and the so-called passport option.
