Arbitrage Problems with Reflected Geometric Brownian Motion

Abstract

Contrary to the claims made by several authors, a financial market model in which the price of a risky security follows a reflected geometric Brownian motion is not arbitrage-free.In fact, such a model is unsuitable for contingent claim valuation because it violates even the weakest no-arbitrage conditions. In particular, it does not admit a well-defined market price of risk, let alone a numéraire portfolio or an equivalent risk-neutral probability measure. Moreover, the published option pricing formulae for such models violate textbook no-arbitrage bounds.