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Arbitrage problems with reflected geometric Brownian motion

Buckner, Dean; Dowd, Kevin; Hulley, Hardy

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Dean Buckner

Hardy Hulley


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 numéraire portfolios or equivalent risk-neutral probability measures, which makes them unsuitable for contingent claim valuation. Unsurprisingly, the published option pricing formulae for such models violate classical no-arbitrage bounds.


Buckner, D., Dowd, K., & Hulley, H. (2024). Arbitrage problems with reflected geometric Brownian motion. Finance and Stochastics, 28(1), 1-26.

Journal Article Type Article
Acceptance Date Aug 23, 2023
Online Publication Date Dec 20, 2023
Publication Date Jan 1, 2024
Deposit Date Aug 24, 2023
Publicly Available Date Jan 4, 2024
Journal Finance and Stochastics
Print ISSN 0949-2984
Electronic ISSN 1432-1122
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 28
Issue 1
Pages 1-26
Keywords Local time, Contingent claim valuation, 91G15, C6, G12, 91G16, Arbitrage, G13, 60H10, Reflected geometric Brownian motion
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