Arbitrage Problems with Reflected Geometric Brownian Motion
Mathematical Finance
2022-09-07 v2
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 models violate even the weakest no-arbitrage condition considered in the literature. Consequently, they do not admit num\'eraire portfolios or equivalent risk-neutral probability measures, which makes them totally unsuitable for contingent claim valuation. Unsurprisingly, the published option pricing formulae for such models violate textbook no-arbitrage bounds.
Keywords
Cite
@article{arxiv.2201.05312,
title = {Arbitrage Problems with Reflected Geometric Brownian Motion},
author = {Dean Buckner and Kevin Dowd and Hardy Hulley},
journal= {arXiv preprint arXiv:2201.05312},
year = {2022}
}