Valuing stock options when prices are subject to a lower boundary

Abstract

Abstract This study examines the implications for stock option pricing when the domain of the stock price is constrained by a lower boundary. The valuation strategy starts from the familiar geometric Brownian motion framework of Black & Scholes (1973). However, an instantaneously reflecting lower boundary will be superimposed such that a reflected geometric Brownian motion arises. The particular nature of reflection in this approach precludes arbitrage opportunities such that risk‐neutral option valuation techniques can straightforwardly be applied. It will be shown that ignoring lower boundaries can lead to a substantial undervaluation of option prices. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:231–247, 2008