Analytical American Option Pricing: The Flat‐barrier Lower Bound*

Abstract

In a Black and Scholes (1973) world, this paper studies the pricing performance of a closed‐form lower bound to American option values based on an exercise strategy corresponding to a flat‐exercise boundary. The lower bound has a simple two‐step implementation akin to Barone‐Adesi and Whaley (1987) formula and shows superior pricing performance in the out‐of‐the‐money region and for long maturities.

Pricing American Options under the Constant Elasticity of Variance Model and Subject to Bankruptcy

“…Assuming a convenient parametric specification for the barrier function E t , it is possible to convert equation (6a) into a closed-form solution. Such an approach was pursued, for instance, by Ingersoll (1998), using both constant and exponential specifications, and by Sbuelz (2004), also under a constant barrier formulation. Unfortunately, the time path {E t , t 0 ≤ t ≤ T} of critical asset prices, which is called the exercise boundary, is not known ex ante, and therefore the assumption of a specific parametric form for the barrier function simply transforms equation (6a) into a lower bound for the true American put option value.…”

“…This is the simplest specification one can adopt and has already been used by Ingersoll (1998) and Sbuelz (2004) under the geometric Brownian motion assumption. Although it yields a closed-form solution for equation (11), such an exercise boundary cannot simultaneously satisfy previously stated requirements iii) and iv).…”