Valuing stock options when prices are subject to a lower boundary

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