Analytical Approximations for American Options: The Binary Power Option Approach

Abstract

This study proposes an innovative approach to value American options. Using a portfolio of binary power options to replicate the early exercise premium, we modify Medvedev and Scaillet (2010) to derive an analytical approximation of American option values under the Black-Scholes framework. Compared with Medvedev and Scaillet (2010), our approach provides a much simpler functional form of the early exercise premium that can be easily extended to high-order series expansions. The numerical results show that the pricing performance of our method is closely comparable to that of Medvedev and Scaillet (2010) and superior to that of Barone-Adesi and Whaley (1987).