On the quadratic approximation to the value of American put options: a note

Abstract

This article extends the quasi-analytical quadratic approximation of Barone-Adesi and Whaley (1987) in order to improve its performance for options with long time to expiration. We build a system of equations with an extra parameter and an additional boundary condition (‘boundary-optimality’), ensuring that the derived exercise boundary maximizes the price of the option. Numerical results for this approach show improved convergence performance for the quadratic approximation in the case of longer option lives.