Americans are Europeans in Disguise

Abstract

In this paper, we prove, in the context of the Black-Scholes-Merton model, that the price of the American put option in the continuation region is equal to that of a European option with an equivalent payoff. We discuss the extension of the result for other one-dimensional option pricing models. We also develop a numerical procedure to approximate the equivalent European payoff and conduct a numerical experiment spanning a wide range of parameters of the Black-Scholes-Merton model and contract characteristics. Overall, the method produces American option prices with a relative RMSE close to 0.001% compared to a benchmark.

Keywords: American options, European options, Black-Scholes-Merton model, models with jumps

JEL Classification: C63, G13