Pricing Multidimensional American Options

Abstract

A new explicit form is provided for the solution of optimal stopping problems involving a multidimensional geometric Brownian motion. A free-boundary value approach is adopted and the value function is obtained via fundamental solution methods. There are many applications for the valuation of perpetual options of American style, which are of interest for finance and managerial decisions.

Keywords

• American options
• optimal exercise boundary
• multidimensional stochastic processes
• optimal stopping